Dataset Viewer
nums
sequencelengths 4
4
| target
int64 10
100
| solution
sequencelengths 3
3
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float64 0
1
| search_type
stringclasses 2
values | heuristic
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value | messages_optimal
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[
90,
11,
37,
95
] | 55 |
[
"90+95=185",
"11*185=2035",
"2035/37=55"
] | 0.813368 |
dfs
|
sum_heuristic
|
[
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Current State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+95=185, Resulting Numbers: [11, 37, 185]\nGenerated Node #2: [11, 37, 185] from Operation: 90+95=185\nCurrent State: 55:[11, 37, 185], Operations: ['90+95=185']\nExploring Operation: 11*185=2035, Resulting Numbers: [37, 2035]\nGenerated Node #3: [37, 2035] from Operation: 11*185=2035\nCurrent State: 55:[37, 2035], Operations: ['90+95=185', '11*185=2035']\nExploring Operation: 2035/37=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['90+95=185', '11*185=2035', '2035/37=55']\nRESULT: 55\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [90, 11, 37, 95]. Our goal is to produce 55. Let's show the search process step by step:\nOne possible strategy is to use a Depth-First Search (DFS) guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [37, 95, 79].\nHeuristic score : (|37-55| + |95-55| + |79-55|)/3 = (18 + 40 + 24)/3 = 27.33\nGenerated Node #0,0: 55:[37, 95, 79] Operation: 90-11=79\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [79, 58].\nHeuristic score : (|79-55| + |58-55|)/2 = (24 + 3)/2 = 13.50\nGenerated Node #0,0,0: 55:[79, 58] Operation: 95-37=58\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 79-58=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 79-37=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,0,1: 55:[95, 42] Operation: 79-37=42\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 95-79=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,0,2: 55:[37, 16] Operation: 95-79=16\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 4th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [79, 132].\nHeuristic score : (|79-55| + |132-55|)/2 = (24 + 77)/2 = 50.50\nGenerated Node #0,0,3: 55:[79, 132] Operation: 37+95=132\n\nThought : Expand Node #0,0,3’s 1st child to build next frontier.\nAction : Exploring operation 132-79=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 5th child to build next frontier.\nAction : Exploring operation 37+79=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,0,4: 55:[95, 116] Operation: 37+79=116\n\nThought : Expand Node #0,0,4’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 6th child to build next frontier.\nAction : Exploring operation 95+79=174. \nResulting numbers: [37, 174].\nHeuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\nGenerated Node #0,0,5: 55:[37, 174] Operation: 95+79=174\n\nThought : Expand Node #0,0,5’s 1st child to build next frontier.\nAction : Exploring operation 174-37=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 7th child to build next frontier.\nAction : Exploring operation 37*79=2923. \nResulting numbers: [95, 2923].\nHeuristic score : (|95-55| + |2923-55|)/2 = (40 + 2868)/2 = 1454.00\nGenerated Node #0,0,6: 55:[95, 2923] Operation: 37*79=2923\n\nThought : Expand Node #0,0,6’s 1st child to build next frontier.\nAction : Exploring operation 2923-95=2828. \nResulting numbers: [2828].\n2828,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 8th child to build next frontier.\nAction : Exploring operation 37*95=3515. \nResulting numbers: [79, 3515].\nHeuristic score : (|79-55| + |3515-55|)/2 = (24 + 3460)/2 = 1742.00\nGenerated Node #0,0,7: 55:[79, 3515] Operation: 37*95=3515\n\nThought : Expand Node #0,0,7’s 1st child to build next frontier.\nAction : Exploring operation 3515-79=3436. \nResulting numbers: [3436].\n3436,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 27.333333333333332\nCurrent State #0,0: 55:[37, 95, 79]. Operations so far : ['90-11=79'].\n\nThought : Expand Node #0,0’s 9th child to build next frontier.\nAction : Exploring operation 95*79=7505. \nResulting numbers: [37, 7505].\nHeuristic score : (|37-55| + |7505-55|)/2 = (18 + 7450)/2 = 3734.00\nGenerated Node #0,0,8: 55:[37, 7505] Operation: 95*79=7505\n\nThought : Expand Node #0,0,8’s 1st child to build next frontier.\nAction : Exploring operation 7505-37=7468. \nResulting numbers: [7468].\n7468,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 2nd child to build next frontier.\nAction : Exploring operation 11+37=48. \nResulting numbers: [90, 95, 48].\nHeuristic score : (|90-55| + |95-55| + |48-55|)/3 = (35 + 40 + 7)/3 = 27.33\nGenerated Node #0,1: 55:[90, 95, 48] Operation: 11+37=48\n\nThought : Expand Node #0,1’s 1st child to build next frontier.\nAction : Exploring operation 95-48=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,1,0: 55:[90, 47] Operation: 95-48=47\n\nThought : Expand Node #0,1,0’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 2nd child to build next frontier.\nAction : Exploring operation 90-48=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,1,1: 55:[95, 42] Operation: 90-48=42\n\nThought : Expand Node #0,1,1’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 3rd child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [48, 5].\nHeuristic score : (|48-55| + |5-55|)/2 = (7 + 50)/2 = 28.50\nGenerated Node #0,1,2: 55:[48, 5] Operation: 95-90=5\n\nThought : Expand Node #0,1,2’s 1st child to build next frontier.\nAction : Exploring operation 48+5=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 4th child to build next frontier.\nAction : Exploring operation 90+48=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,1,3: 55:[95, 138] Operation: 90+48=138\n\nThought : Expand Node #0,1,3’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 5th child to build next frontier.\nAction : Exploring operation 95+48=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,1,4: 55:[90, 143] Operation: 95+48=143\n\nThought : Expand Node #0,1,4’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 6th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [48, 185].\nHeuristic score : (|48-55| + |185-55|)/2 = (7 + 130)/2 = 68.50\nGenerated Node #0,1,5: 55:[48, 185] Operation: 90+95=185\n\nThought : Expand Node #0,1,5’s 1st child to build next frontier.\nAction : Exploring operation 185-48=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 7th child to build next frontier.\nAction : Exploring operation 90*48=4320. \nResulting numbers: [95, 4320].\nHeuristic score : (|95-55| + |4320-55|)/2 = (40 + 4265)/2 = 2152.50\nGenerated Node #0,1,6: 55:[95, 4320] Operation: 90*48=4320\n\nThought : Expand Node #0,1,6’s 1st child to build next frontier.\nAction : Exploring operation 4320-95=4225. \nResulting numbers: [4225].\n4225,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 8th child to build next frontier.\nAction : Exploring operation 95*48=4560. \nResulting numbers: [90, 4560].\nHeuristic score : (|90-55| + |4560-55|)/2 = (35 + 4505)/2 = 2270.00\nGenerated Node #0,1,7: 55:[90, 4560] Operation: 95*48=4560\n\nThought : Expand Node #0,1,7’s 1st child to build next frontier.\nAction : Exploring operation 4560-90=4470. \nResulting numbers: [4470].\n4470,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,1 with lowest heuristic value 27.333333333333332\nCurrent State #0,1: 55:[90, 95, 48]. Operations so far : ['11+37=48'].\n\nThought : Expand Node #0,1’s 9th child to build next frontier.\nAction : Exploring operation 90*95=8550. \nResulting numbers: [48, 8550].\nHeuristic score : (|48-55| + |8550-55|)/2 = (7 + 8495)/2 = 4251.00\nGenerated Node #0,1,8: 55:[48, 8550] Operation: 90*95=8550\n\nThought : Expand Node #0,1,8’s 1st child to build next frontier.\nAction : Exploring operation 8550-48=8502. \nResulting numbers: [8502].\n8502,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 3rd child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [90, 37, 84].\nHeuristic score : (|90-55| + |37-55| + |84-55|)/3 = (35 + 18 + 29)/3 = 27.33\nGenerated Node #0,2: 55:[90, 37, 84] Operation: 95-11=84\n\nThought : Expand Node #0,2’s 1st child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [84, 53].\nHeuristic score : (|84-55| + |53-55|)/2 = (29 + 2)/2 = 15.50\nGenerated Node #0,2,0: 55:[84, 53] Operation: 90-37=53\n\nThought : Expand Node #0,2,0’s 1st child to build next frontier.\nAction : Exploring operation 84-53=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 2nd child to build next frontier.\nAction : Exploring operation 84-37=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,2,1: 55:[90, 47] Operation: 84-37=47\n\nThought : Expand Node #0,2,1’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 3rd child to build next frontier.\nAction : Exploring operation 90-84=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,2,2: 55:[37, 6] Operation: 90-84=6\n\nThought : Expand Node #0,2,2’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 4th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [84, 127].\nHeuristic score : (|84-55| + |127-55|)/2 = (29 + 72)/2 = 50.50\nGenerated Node #0,2,3: 55:[84, 127] Operation: 90+37=127\n\nThought : Expand Node #0,2,3’s 1st child to build next frontier.\nAction : Exploring operation 127-84=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 5th child to build next frontier.\nAction : Exploring operation 37+84=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,2,4: 55:[90, 121] Operation: 37+84=121\n\nThought : Expand Node #0,2,4’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 6th child to build next frontier.\nAction : Exploring operation 90+84=174. \nResulting numbers: [37, 174].\nHeuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\nGenerated Node #0,2,5: 55:[37, 174] Operation: 90+84=174\n\nThought : Expand Node #0,2,5’s 1st child to build next frontier.\nAction : Exploring operation 174-37=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 7th child to build next frontier.\nAction : Exploring operation 37*84=3108. \nResulting numbers: [90, 3108].\nHeuristic score : (|90-55| + |3108-55|)/2 = (35 + 3053)/2 = 1544.00\nGenerated Node #0,2,6: 55:[90, 3108] Operation: 37*84=3108\n\nThought : Expand Node #0,2,6’s 1st child to build next frontier.\nAction : Exploring operation 3108-90=3018. \nResulting numbers: [3018].\n3018,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 8th child to build next frontier.\nAction : Exploring operation 90*37=3330. \nResulting numbers: [84, 3330].\nHeuristic score : (|84-55| + |3330-55|)/2 = (29 + 3275)/2 = 1652.00\nGenerated Node #0,2,7: 55:[84, 3330] Operation: 90*37=3330\n\nThought : Expand Node #0,2,7’s 1st child to build next frontier.\nAction : Exploring operation 3330-84=3246. \nResulting numbers: [3246].\n3246,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,2 with lowest heuristic value 27.333333333333332\nCurrent State #0,2: 55:[90, 37, 84]. Operations so far : ['95-11=84'].\n\nThought : Expand Node #0,2’s 9th child to build next frontier.\nAction : Exploring operation 90*84=7560. \nResulting numbers: [37, 7560].\nHeuristic score : (|37-55| + |7560-55|)/2 = (18 + 7505)/2 = 3761.50\nGenerated Node #0,2,8: 55:[37, 7560] Operation: 90*84=7560\n\nThought : Expand Node #0,2,8’s 1st child to build next frontier.\nAction : Exploring operation 7560-37=7523. \nResulting numbers: [7523].\n7523,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 4th child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [90, 11, 58].\nHeuristic score : (|90-55| + |11-55| + |58-55|)/3 = (35 + 44 + 3)/3 = 27.33\nGenerated Node #0,3: 55:[90, 11, 58] Operation: 95-37=58\n\nThought : Expand Node #0,3’s 1st child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [58, 79].\nHeuristic score : (|58-55| + |79-55|)/2 = (3 + 24)/2 = 13.50\nGenerated Node #0,3,0: 55:[58, 79] Operation: 90-11=79\n\nThought : Expand Node #0,3,0’s 1st child to build next frontier.\nAction : Exploring operation 79-58=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 2nd child to build next frontier.\nAction : Exploring operation 58-11=47. \nResulting numbers: [90, 47].\nHeuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\nGenerated Node #0,3,1: 55:[90, 47] Operation: 58-11=47\n\nThought : Expand Node #0,3,1’s 1st child to build next frontier.\nAction : Exploring operation 90-47=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 3rd child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [58, 101].\nHeuristic score : (|58-55| + |101-55|)/2 = (3 + 46)/2 = 24.50\nGenerated Node #0,3,2: 55:[58, 101] Operation: 90+11=101\n\nThought : Expand Node #0,3,2’s 1st child to build next frontier.\nAction : Exploring operation 101-58=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 4th child to build next frontier.\nAction : Exploring operation 11+58=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,3,3: 55:[90, 69] Operation: 11+58=69\n\nThought : Expand Node #0,3,3’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 5th child to build next frontier.\nAction : Exploring operation 90-58=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,3,4: 55:[11, 32] Operation: 90-58=32\n\nThought : Expand Node #0,3,4’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 6th child to build next frontier.\nAction : Exploring operation 90+58=148. \nResulting numbers: [11, 148].\nHeuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\nGenerated Node #0,3,5: 55:[11, 148] Operation: 90+58=148\n\nThought : Expand Node #0,3,5’s 1st child to build next frontier.\nAction : Exploring operation 148-11=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 7th child to build next frontier.\nAction : Exploring operation 11*58=638. \nResulting numbers: [90, 638].\nHeuristic score : (|90-55| + |638-55|)/2 = (35 + 583)/2 = 309.00\nGenerated Node #0,3,6: 55:[90, 638] Operation: 11*58=638\n\nThought : Expand Node #0,3,6’s 1st child to build next frontier.\nAction : Exploring operation 638-90=548. \nResulting numbers: [548].\n548,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 8th child to build next frontier.\nAction : Exploring operation 90*11=990. \nResulting numbers: [58, 990].\nHeuristic score : (|58-55| + |990-55|)/2 = (3 + 935)/2 = 469.00\nGenerated Node #0,3,7: 55:[58, 990] Operation: 90*11=990\n\nThought : Expand Node #0,3,7’s 1st child to build next frontier.\nAction : Exploring operation 990-58=932. \nResulting numbers: [932].\n932,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,3 with lowest heuristic value 27.333333333333332\nCurrent State #0,3: 55:[90, 11, 58]. Operations so far : ['95-37=58'].\n\nThought : Expand Node #0,3’s 9th child to build next frontier.\nAction : Exploring operation 90*58=5220. \nResulting numbers: [11, 5220].\nHeuristic score : (|11-55| + |5220-55|)/2 = (44 + 5165)/2 = 2604.50\nGenerated Node #0,3,8: 55:[11, 5220] Operation: 90*58=5220\n\nThought : Expand Node #0,3,8’s 1st child to build next frontier.\nAction : Exploring operation 5220-11=5209. \nResulting numbers: [5209].\n5209,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 5th child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [11, 95, 53].\nHeuristic score : (|11-55| + |95-55| + |53-55|)/3 = (44 + 40 + 2)/3 = 28.67\nGenerated Node #0,4: 55:[11, 95, 53] Operation: 90-37=53\n\nThought : Expand Node #0,4’s 1st child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [53, 84].\nHeuristic score : (|53-55| + |84-55|)/2 = (2 + 29)/2 = 15.50\nGenerated Node #0,4,0: 55:[53, 84] Operation: 95-11=84\n\nThought : Expand Node #0,4,0’s 1st child to build next frontier.\nAction : Exploring operation 84-53=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 2nd child to build next frontier.\nAction : Exploring operation 11+53=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,4,1: 55:[95, 64] Operation: 11+53=64\n\nThought : Expand Node #0,4,1’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 3rd child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [53, 106].\nHeuristic score : (|53-55| + |106-55|)/2 = (2 + 51)/2 = 26.50\nGenerated Node #0,4,2: 55:[53, 106] Operation: 11+95=106\n\nThought : Expand Node #0,4,2’s 1st child to build next frontier.\nAction : Exploring operation 106-53=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 4th child to build next frontier.\nAction : Exploring operation 53-11=42. \nResulting numbers: [95, 42].\nHeuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\nGenerated Node #0,4,3: 55:[95, 42] Operation: 53-11=42\n\nThought : Expand Node #0,4,3’s 1st child to build next frontier.\nAction : Exploring operation 95-42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 5th child to build next frontier.\nAction : Exploring operation 95-53=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,4,4: 55:[11, 42] Operation: 95-53=42\n\nThought : Expand Node #0,4,4’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 6th child to build next frontier.\nAction : Exploring operation 95+53=148. \nResulting numbers: [11, 148].\nHeuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\nGenerated Node #0,4,5: 55:[11, 148] Operation: 95+53=148\n\nThought : Expand Node #0,4,5’s 1st child to build next frontier.\nAction : Exploring operation 148-11=137. \nResulting numbers: [137].\n137,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 7th child to build next frontier.\nAction : Exploring operation 11*53=583. \nResulting numbers: [95, 583].\nHeuristic score : (|95-55| + |583-55|)/2 = (40 + 528)/2 = 284.00\nGenerated Node #0,4,6: 55:[95, 583] Operation: 11*53=583\n\nThought : Expand Node #0,4,6’s 1st child to build next frontier.\nAction : Exploring operation 583-95=488. \nResulting numbers: [488].\n488,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 8th child to build next frontier.\nAction : Exploring operation 11*95=1045. \nResulting numbers: [53, 1045].\nHeuristic score : (|53-55| + |1045-55|)/2 = (2 + 990)/2 = 496.00\nGenerated Node #0,4,7: 55:[53, 1045] Operation: 11*95=1045\n\nThought : Expand Node #0,4,7’s 1st child to build next frontier.\nAction : Exploring operation 1045-53=992. \nResulting numbers: [992].\n992,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,4 with lowest heuristic value 28.666666666666668\nCurrent State #0,4: 55:[11, 95, 53]. Operations so far : ['90-37=53'].\n\nThought : Expand Node #0,4’s 9th child to build next frontier.\nAction : Exploring operation 95*53=5035. \nResulting numbers: [11, 5035].\nHeuristic score : (|11-55| + |5035-55|)/2 = (44 + 4980)/2 = 2512.00\nGenerated Node #0,4,8: 55:[11, 5035] Operation: 95*53=5035\n\nThought : Expand Node #0,4,8’s 1st child to build next frontier.\nAction : Exploring operation 5035-11=5024. \nResulting numbers: [5024].\n5024,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 6th child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [37, 95, 101].\nHeuristic score : (|37-55| + |95-55| + |101-55|)/3 = (18 + 40 + 46)/3 = 34.67\nGenerated Node #0,5: 55:[37, 95, 101] Operation: 90+11=101\n\nThought : Expand Node #0,5’s 1st child to build next frontier.\nAction : Exploring operation 95-37=58. \nResulting numbers: [101, 58].\nHeuristic score : (|101-55| + |58-55|)/2 = (46 + 3)/2 = 24.50\nGenerated Node #0,5,0: 55:[101, 58] Operation: 95-37=58\n\nThought : Expand Node #0,5,0’s 1st child to build next frontier.\nAction : Exploring operation 101-58=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 2nd child to build next frontier.\nAction : Exploring operation 101-37=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,5,1: 55:[95, 64] Operation: 101-37=64\n\nThought : Expand Node #0,5,1’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 3rd child to build next frontier.\nAction : Exploring operation 101-95=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,5,2: 55:[37, 6] Operation: 101-95=6\n\nThought : Expand Node #0,5,2’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 4th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [101, 132].\nHeuristic score : (|101-55| + |132-55|)/2 = (46 + 77)/2 = 61.50\nGenerated Node #0,5,3: 55:[101, 132] Operation: 37+95=132\n\nThought : Expand Node #0,5,3’s 1st child to build next frontier.\nAction : Exploring operation 132-101=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 5th child to build next frontier.\nAction : Exploring operation 37+101=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,5,4: 55:[95, 138] Operation: 37+101=138\n\nThought : Expand Node #0,5,4’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 6th child to build next frontier.\nAction : Exploring operation 95+101=196. \nResulting numbers: [37, 196].\nHeuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\nGenerated Node #0,5,5: 55:[37, 196] Operation: 95+101=196\n\nThought : Expand Node #0,5,5’s 1st child to build next frontier.\nAction : Exploring operation 196-37=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 7th child to build next frontier.\nAction : Exploring operation 37*95=3515. \nResulting numbers: [101, 3515].\nHeuristic score : (|101-55| + |3515-55|)/2 = (46 + 3460)/2 = 1753.00\nGenerated Node #0,5,6: 55:[101, 3515] Operation: 37*95=3515\n\nThought : Expand Node #0,5,6’s 1st child to build next frontier.\nAction : Exploring operation 3515-101=3414. \nResulting numbers: [3414].\n3414,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 8th child to build next frontier.\nAction : Exploring operation 37*101=3737. \nResulting numbers: [95, 3737].\nHeuristic score : (|95-55| + |3737-55|)/2 = (40 + 3682)/2 = 1861.00\nGenerated Node #0,5,7: 55:[95, 3737] Operation: 37*101=3737\n\nThought : Expand Node #0,5,7’s 1st child to build next frontier.\nAction : Exploring operation 3737-95=3642. \nResulting numbers: [3642].\n3642,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,5 with lowest heuristic value 34.666666666666664\nCurrent State #0,5: 55:[37, 95, 101]. Operations so far : ['90+11=101'].\n\nThought : Expand Node #0,5’s 9th child to build next frontier.\nAction : Exploring operation 95*101=9595. \nResulting numbers: [37, 9595].\nHeuristic score : (|37-55| + |9595-55|)/2 = (18 + 9540)/2 = 4779.00\nGenerated Node #0,5,8: 55:[37, 9595] Operation: 95*101=9595\n\nThought : Expand Node #0,5,8’s 1st child to build next frontier.\nAction : Exploring operation 9595-37=9558. \nResulting numbers: [9558].\n9558,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 7th child to build next frontier.\nAction : Exploring operation 37-11=26. \nResulting numbers: [90, 95, 26].\nHeuristic score : (|90-55| + |95-55| + |26-55|)/3 = (35 + 40 + 29)/3 = 34.67\nGenerated Node #0,6: 55:[90, 95, 26] Operation: 37-11=26\n\nThought : Expand Node #0,6’s 1st child to build next frontier.\nAction : Exploring operation 90-26=64. \nResulting numbers: [95, 64].\nHeuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\nGenerated Node #0,6,0: 55:[95, 64] Operation: 90-26=64\n\nThought : Expand Node #0,6,0’s 1st child to build next frontier.\nAction : Exploring operation 95-64=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 2nd child to build next frontier.\nAction : Exploring operation 95-26=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,6,1: 55:[90, 69] Operation: 95-26=69\n\nThought : Expand Node #0,6,1’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 3rd child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [26, 5].\nHeuristic score : (|26-55| + |5-55|)/2 = (29 + 50)/2 = 39.50\nGenerated Node #0,6,2: 55:[26, 5] Operation: 95-90=5\n\nThought : Expand Node #0,6,2’s 1st child to build next frontier.\nAction : Exploring operation 26+5=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 4th child to build next frontier.\nAction : Exploring operation 90+26=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,6,3: 55:[95, 116] Operation: 90+26=116\n\nThought : Expand Node #0,6,3’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 5th child to build next frontier.\nAction : Exploring operation 95+26=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,6,4: 55:[90, 121] Operation: 95+26=121\n\nThought : Expand Node #0,6,4’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 6th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [26, 185].\nHeuristic score : (|26-55| + |185-55|)/2 = (29 + 130)/2 = 79.50\nGenerated Node #0,6,5: 55:[26, 185] Operation: 90+95=185\n\nThought : Expand Node #0,6,5’s 1st child to build next frontier.\nAction : Exploring operation 185-26=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 7th child to build next frontier.\nAction : Exploring operation 90*26=2340. \nResulting numbers: [95, 2340].\nHeuristic score : (|95-55| + |2340-55|)/2 = (40 + 2285)/2 = 1162.50\nGenerated Node #0,6,6: 55:[95, 2340] Operation: 90*26=2340\n\nThought : Expand Node #0,6,6’s 1st child to build next frontier.\nAction : Exploring operation 2340-95=2245. \nResulting numbers: [2245].\n2245,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 8th child to build next frontier.\nAction : Exploring operation 95*26=2470. \nResulting numbers: [90, 2470].\nHeuristic score : (|90-55| + |2470-55|)/2 = (35 + 2415)/2 = 1225.00\nGenerated Node #0,6,7: 55:[90, 2470] Operation: 95*26=2470\n\nThought : Expand Node #0,6,7’s 1st child to build next frontier.\nAction : Exploring operation 2470-90=2380. \nResulting numbers: [2380].\n2380,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,6 with lowest heuristic value 34.666666666666664\nCurrent State #0,6: 55:[90, 95, 26]. Operations so far : ['37-11=26'].\n\nThought : Expand Node #0,6’s 9th child to build next frontier.\nAction : Exploring operation 90*95=8550. \nResulting numbers: [26, 8550].\nHeuristic score : (|26-55| + |8550-55|)/2 = (29 + 8495)/2 = 4262.00\nGenerated Node #0,6,8: 55:[26, 8550] Operation: 90*95=8550\n\nThought : Expand Node #0,6,8’s 1st child to build next frontier.\nAction : Exploring operation 8550-26=8524. \nResulting numbers: [8524].\n8524,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 8th child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [90, 37, 106].\nHeuristic score : (|90-55| + |37-55| + |106-55|)/3 = (35 + 18 + 51)/3 = 34.67\nGenerated Node #0,7: 55:[90, 37, 106] Operation: 11+95=106\n\nThought : Expand Node #0,7’s 1st child to build next frontier.\nAction : Exploring operation 106-37=69. \nResulting numbers: [90, 69].\nHeuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\nGenerated Node #0,7,0: 55:[90, 69] Operation: 106-37=69\n\nThought : Expand Node #0,7,0’s 1st child to build next frontier.\nAction : Exploring operation 90-69=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 2nd child to build next frontier.\nAction : Exploring operation 90-37=53. \nResulting numbers: [106, 53].\nHeuristic score : (|106-55| + |53-55|)/2 = (51 + 2)/2 = 26.50\nGenerated Node #0,7,1: 55:[106, 53] Operation: 90-37=53\n\nThought : Expand Node #0,7,1’s 1st child to build next frontier.\nAction : Exploring operation 106-53=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 3rd child to build next frontier.\nAction : Exploring operation 106-90=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,7,2: 55:[37, 16] Operation: 106-90=16\n\nThought : Expand Node #0,7,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 4th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [106, 127].\nHeuristic score : (|106-55| + |127-55|)/2 = (51 + 72)/2 = 61.50\nGenerated Node #0,7,3: 55:[106, 127] Operation: 90+37=127\n\nThought : Expand Node #0,7,3’s 1st child to build next frontier.\nAction : Exploring operation 127-106=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 5th child to build next frontier.\nAction : Exploring operation 37+106=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,7,4: 55:[90, 143] Operation: 37+106=143\n\nThought : Expand Node #0,7,4’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 6th child to build next frontier.\nAction : Exploring operation 90+106=196. \nResulting numbers: [37, 196].\nHeuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\nGenerated Node #0,7,5: 55:[37, 196] Operation: 90+106=196\n\nThought : Expand Node #0,7,5’s 1st child to build next frontier.\nAction : Exploring operation 196-37=159. \nResulting numbers: [159].\n159,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 7th child to build next frontier.\nAction : Exploring operation 90*37=3330. \nResulting numbers: [106, 3330].\nHeuristic score : (|106-55| + |3330-55|)/2 = (51 + 3275)/2 = 1663.00\nGenerated Node #0,7,6: 55:[106, 3330] Operation: 90*37=3330\n\nThought : Expand Node #0,7,6’s 1st child to build next frontier.\nAction : Exploring operation 3330-106=3224. \nResulting numbers: [3224].\n3224,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 8th child to build next frontier.\nAction : Exploring operation 37*106=3922. \nResulting numbers: [90, 3922].\nHeuristic score : (|90-55| + |3922-55|)/2 = (35 + 3867)/2 = 1951.00\nGenerated Node #0,7,7: 55:[90, 3922] Operation: 37*106=3922\n\nThought : Expand Node #0,7,7’s 1st child to build next frontier.\nAction : Exploring operation 3922-90=3832. \nResulting numbers: [3832].\n3832,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,7 with lowest heuristic value 34.666666666666664\nCurrent State #0,7: 55:[90, 37, 106]. Operations so far : ['11+95=106'].\n\nThought : Expand Node #0,7’s 9th child to build next frontier.\nAction : Exploring operation 90*106=9540. \nResulting numbers: [37, 9540].\nHeuristic score : (|37-55| + |9540-55|)/2 = (18 + 9485)/2 = 4751.50\nGenerated Node #0,7,8: 55:[37, 9540] Operation: 90*106=9540\n\nThought : Expand Node #0,7,8’s 1st child to build next frontier.\nAction : Exploring operation 9540-37=9503. \nResulting numbers: [9503].\n9503,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 9th child to build next frontier.\nAction : Exploring operation 95-90=5. \nResulting numbers: [11, 37, 5].\nHeuristic score : (|11-55| + |37-55| + |5-55|)/3 = (44 + 18 + 50)/3 = 37.33\nGenerated Node #0,8: 55:[11, 37, 5] Operation: 95-90=5\n\nThought : Expand Node #0,8’s 1st child to build next frontier.\nAction : Exploring operation 11*5=55. \nResulting numbers: [37, 55].\nHeuristic score : (|37-55| + |55-55|)/2 = (18 + 0)/2 = 9.00\nGenerated Node #0,8,0: 55:[37, 55] Operation: 11*5=55\n\nThought : Expand Node #0,8,0’s 1st child to build next frontier.\nAction : Exploring operation 37+55=92. \nResulting numbers: [92].\n92,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 2nd child to build next frontier.\nAction : Exploring operation 11+37=48. \nResulting numbers: [5, 48].\nHeuristic score : (|5-55| + |48-55|)/2 = (50 + 7)/2 = 28.50\nGenerated Node #0,8,1: 55:[5, 48] Operation: 11+37=48\n\nThought : Expand Node #0,8,1’s 1st child to build next frontier.\nAction : Exploring operation 5+48=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 3rd child to build next frontier.\nAction : Exploring operation 11+5=16. \nResulting numbers: [37, 16].\nHeuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\nGenerated Node #0,8,2: 55:[37, 16] Operation: 11+5=16\n\nThought : Expand Node #0,8,2’s 1st child to build next frontier.\nAction : Exploring operation 37+16=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 4th child to build next frontier.\nAction : Exploring operation 37+5=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,8,3: 55:[11, 42] Operation: 37+5=42\n\nThought : Expand Node #0,8,3’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 5th child to build next frontier.\nAction : Exploring operation 11-5=6. \nResulting numbers: [37, 6].\nHeuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\nGenerated Node #0,8,4: 55:[37, 6] Operation: 11-5=6\n\nThought : Expand Node #0,8,4’s 1st child to build next frontier.\nAction : Exploring operation 37+6=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 6th child to build next frontier.\nAction : Exploring operation 37-5=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,8,5: 55:[11, 32] Operation: 37-5=32\n\nThought : Expand Node #0,8,5’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 7th child to build next frontier.\nAction : Exploring operation 37-11=26. \nResulting numbers: [5, 26].\nHeuristic score : (|5-55| + |26-55|)/2 = (50 + 29)/2 = 39.50\nGenerated Node #0,8,6: 55:[5, 26] Operation: 37-11=26\n\nThought : Expand Node #0,8,6’s 1st child to build next frontier.\nAction : Exploring operation 5+26=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 8th child to build next frontier.\nAction : Exploring operation 37*5=185. \nResulting numbers: [11, 185].\nHeuristic score : (|11-55| + |185-55|)/2 = (44 + 130)/2 = 87.00\nGenerated Node #0,8,7: 55:[11, 185] Operation: 37*5=185\n\nThought : Expand Node #0,8,7’s 1st child to build next frontier.\nAction : Exploring operation 185-11=174. \nResulting numbers: [174].\n174,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,8 with lowest heuristic value 37.333333333333336\nCurrent State #0,8: 55:[11, 37, 5]. Operations so far : ['95-90=5'].\n\nThought : Expand Node #0,8’s 9th child to build next frontier.\nAction : Exploring operation 11*37=407. \nResulting numbers: [5, 407].\nHeuristic score : (|5-55| + |407-55|)/2 = (50 + 352)/2 = 201.00\nGenerated Node #0,8,8: 55:[5, 407] Operation: 11*37=407\n\nThought : Expand Node #0,8,8’s 1st child to build next frontier.\nAction : Exploring operation 407-5=402. \nResulting numbers: [402].\n402,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 10th child to build next frontier.\nAction : Exploring operation 90+37=127. \nResulting numbers: [11, 95, 127].\nHeuristic score : (|11-55| + |95-55| + |127-55|)/3 = (44 + 40 + 72)/3 = 52.00\nGenerated Node #0,9: 55:[11, 95, 127] Operation: 90+37=127\n\nThought : Expand Node #0,9’s 1st child to build next frontier.\nAction : Exploring operation 127-95=32. \nResulting numbers: [11, 32].\nHeuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\nGenerated Node #0,9,0: 55:[11, 32] Operation: 127-95=32\n\nThought : Expand Node #0,9,0’s 1st child to build next frontier.\nAction : Exploring operation 11+32=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 2nd child to build next frontier.\nAction : Exploring operation 95-11=84. \nResulting numbers: [127, 84].\nHeuristic score : (|127-55| + |84-55|)/2 = (72 + 29)/2 = 50.50\nGenerated Node #0,9,1: 55:[127, 84] Operation: 95-11=84\n\nThought : Expand Node #0,9,1’s 1st child to build next frontier.\nAction : Exploring operation 127-84=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 3rd child to build next frontier.\nAction : Exploring operation 127-11=116. \nResulting numbers: [95, 116].\nHeuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\nGenerated Node #0,9,2: 55:[95, 116] Operation: 127-11=116\n\nThought : Expand Node #0,9,2’s 1st child to build next frontier.\nAction : Exploring operation 116-95=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 4th child to build next frontier.\nAction : Exploring operation 11+95=106. \nResulting numbers: [127, 106].\nHeuristic score : (|127-55| + |106-55|)/2 = (72 + 51)/2 = 61.50\nGenerated Node #0,9,3: 55:[127, 106] Operation: 11+95=106\n\nThought : Expand Node #0,9,3’s 1st child to build next frontier.\nAction : Exploring operation 127-106=21. \nResulting numbers: [21].\n21,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 5th child to build next frontier.\nAction : Exploring operation 11+127=138. \nResulting numbers: [95, 138].\nHeuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\nGenerated Node #0,9,4: 55:[95, 138] Operation: 11+127=138\n\nThought : Expand Node #0,9,4’s 1st child to build next frontier.\nAction : Exploring operation 138-95=43. \nResulting numbers: [43].\n43,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 6th child to build next frontier.\nAction : Exploring operation 95+127=222. \nResulting numbers: [11, 222].\nHeuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\nGenerated Node #0,9,5: 55:[11, 222] Operation: 95+127=222\n\nThought : Expand Node #0,9,5’s 1st child to build next frontier.\nAction : Exploring operation 222-11=211. \nResulting numbers: [211].\n211,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 7th child to build next frontier.\nAction : Exploring operation 11*95=1045. \nResulting numbers: [127, 1045].\nHeuristic score : (|127-55| + |1045-55|)/2 = (72 + 990)/2 = 531.00\nGenerated Node #0,9,6: 55:[127, 1045] Operation: 11*95=1045\n\nThought : Expand Node #0,9,6’s 1st child to build next frontier.\nAction : Exploring operation 1045-127=918. \nResulting numbers: [918].\n918,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 8th child to build next frontier.\nAction : Exploring operation 11*127=1397. \nResulting numbers: [95, 1397].\nHeuristic score : (|95-55| + |1397-55|)/2 = (40 + 1342)/2 = 691.00\nGenerated Node #0,9,7: 55:[95, 1397] Operation: 11*127=1397\n\nThought : Expand Node #0,9,7’s 1st child to build next frontier.\nAction : Exploring operation 1397-95=1302. \nResulting numbers: [1302].\n1302,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,9 with lowest heuristic value 52.0\nCurrent State #0,9: 55:[11, 95, 127]. Operations so far : ['90+37=127'].\n\nThought : Expand Node #0,9’s 9th child to build next frontier.\nAction : Exploring operation 95*127=12065. \nResulting numbers: [11, 12065].\nHeuristic score : (|11-55| + |12065-55|)/2 = (44 + 12010)/2 = 6027.00\nGenerated Node #0,9,8: 55:[11, 12065] Operation: 95*127=12065\n\nThought : Expand Node #0,9,8’s 1st child to build next frontier.\nAction : Exploring operation 12065-11=12054. \nResulting numbers: [12054].\n12054,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 11th child to build next frontier.\nAction : Exploring operation 37+95=132. \nResulting numbers: [90, 11, 132].\nHeuristic score : (|90-55| + |11-55| + |132-55|)/3 = (35 + 44 + 77)/3 = 52.00\nGenerated Node #0,10: 55:[90, 11, 132] Operation: 37+95=132\n\nThought : Expand Node #0,10’s 1st child to build next frontier.\nAction : Exploring operation 132-90=42. \nResulting numbers: [11, 42].\nHeuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\nGenerated Node #0,10,0: 55:[11, 42] Operation: 132-90=42\n\nThought : Expand Node #0,10,0’s 1st child to build next frontier.\nAction : Exploring operation 11+42=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 2nd child to build next frontier.\nAction : Exploring operation 132/11=12. \nResulting numbers: [90, 12].\nHeuristic score : (|90-55| + |12-55|)/2 = (35 + 43)/2 = 39.00\nGenerated Node #0,10,1: 55:[90, 12] Operation: 132/11=12\n\nThought : Expand Node #0,10,1’s 1st child to build next frontier.\nAction : Exploring operation 90-12=78. \nResulting numbers: [78].\n78,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 3rd child to build next frontier.\nAction : Exploring operation 90-11=79. \nResulting numbers: [132, 79].\nHeuristic score : (|132-55| + |79-55|)/2 = (77 + 24)/2 = 50.50\nGenerated Node #0,10,2: 55:[132, 79] Operation: 90-11=79\n\nThought : Expand Node #0,10,2’s 1st child to build next frontier.\nAction : Exploring operation 132-79=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 4th child to build next frontier.\nAction : Exploring operation 132-11=121. \nResulting numbers: [90, 121].\nHeuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\nGenerated Node #0,10,3: 55:[90, 121] Operation: 132-11=121\n\nThought : Expand Node #0,10,3’s 1st child to build next frontier.\nAction : Exploring operation 121-90=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 5th child to build next frontier.\nAction : Exploring operation 90+11=101. \nResulting numbers: [132, 101].\nHeuristic score : (|132-55| + |101-55|)/2 = (77 + 46)/2 = 61.50\nGenerated Node #0,10,4: 55:[132, 101] Operation: 90+11=101\n\nThought : Expand Node #0,10,4’s 1st child to build next frontier.\nAction : Exploring operation 132-101=31. \nResulting numbers: [31].\n31,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 6th child to build next frontier.\nAction : Exploring operation 11+132=143. \nResulting numbers: [90, 143].\nHeuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\nGenerated Node #0,10,5: 55:[90, 143] Operation: 11+132=143\n\nThought : Expand Node #0,10,5’s 1st child to build next frontier.\nAction : Exploring operation 143-90=53. \nResulting numbers: [53].\n53,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 7th child to build next frontier.\nAction : Exploring operation 90+132=222. \nResulting numbers: [11, 222].\nHeuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\nGenerated Node #0,10,6: 55:[11, 222] Operation: 90+132=222\n\nThought : Expand Node #0,10,6’s 1st child to build next frontier.\nAction : Exploring operation 222-11=211. \nResulting numbers: [211].\n211,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 8th child to build next frontier.\nAction : Exploring operation 90*11=990. \nResulting numbers: [132, 990].\nHeuristic score : (|132-55| + |990-55|)/2 = (77 + 935)/2 = 506.00\nGenerated Node #0,10,7: 55:[132, 990] Operation: 90*11=990\n\nThought : Expand Node #0,10,7’s 1st child to build next frontier.\nAction : Exploring operation 990-132=858. \nResulting numbers: [858].\n858,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 9th child to build next frontier.\nAction : Exploring operation 11*132=1452. \nResulting numbers: [90, 1452].\nHeuristic score : (|90-55| + |1452-55|)/2 = (35 + 1397)/2 = 716.00\nGenerated Node #0,10,8: 55:[90, 1452] Operation: 11*132=1452\n\nThought : Expand Node #0,10,8’s 1st child to build next frontier.\nAction : Exploring operation 1452-90=1362. \nResulting numbers: [1362].\n1362,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,10 with lowest heuristic value 52.0\nCurrent State #0,10: 55:[90, 11, 132]. Operations so far : ['37+95=132'].\n\nThought : Expand Node #0,10’s 10th child to build next frontier.\nAction : Exploring operation 90*132=11880. \nResulting numbers: [11, 11880].\nHeuristic score : (|11-55| + |11880-55|)/2 = (44 + 11825)/2 = 5934.50\nGenerated Node #0,10,9: 55:[11, 11880] Operation: 90*132=11880\n\nThought : Expand Node #0,10,9’s 1st child to build next frontier.\nAction : Exploring operation 11880/11=1080. \nResulting numbers: [1080].\n1080,55 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0 with lowest heuristic value 34.25\nCurrent State #0: 55:[90, 11, 37, 95]. Operations so far : [].\n\nThought : Expand Node #0’s 12th child to build next frontier.\nAction : Exploring operation 90+95=185. \nResulting numbers: [11, 37, 185].\nHeuristic score : (|11-55| + |37-55| + |185-55|)/3 = (44 + 18 + 130)/3 = 64.00\nGenerated Node #0,11: 55:[11, 37, 185] Operation: 90+95=185\n\nThought : Expand Node #0,11’s 1st child to build next frontier.\nAction : Exploring operation 185/37=5. \nResulting numbers: [11, 5].\nHeuristic score : (|11-55| + |5-55|)/2 = (44 + 50)/2 = 47.00\nGenerated Node #0,11,0: 55:[11, 5] Operation: 185/37=5\n\nThought : Expand Node #0,11,0’s 1st child to build next frontier.\nAction : Exploring operation 11*5=55. \nResulting numbers: [55].\n55,55 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['90+95=185', '185/37=5', '11*5=55']\nRESULT: 55\n```\n",
"role": "assistant"
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[
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
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{
"content": "Current State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90-11=79, Resulting Numbers: [37, 95, 79], Heuristic score : (|37-55| + |95-55| + |79-55|)/3 = (18 + 40 + 24)/3 = 27.33\n\nGenerated Node #0,0: 55:[37, 95, 79], Operation: 90-11=79\nExploring Operation: 95-37=58, Resulting Numbers: [79, 58], Heuristic score : (|79-55| + |58-55|)/2 = (24 + 3)/2 = 13.50\n\nGenerated Node #0,0,0: 55:[79, 58], Operation: 95-37=58\nExploring Operation: 79-58=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 79-37=42, Resulting Numbers: [95, 42], Heuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\n\nGenerated Node #0,0,1: 55:[95, 42], Operation: 79-37=42\nExploring Operation: 95-42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95-79=16, Resulting Numbers: [37, 16], Heuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\n\nGenerated Node #0,0,2: 55:[37, 16], Operation: 95-79=16\nExploring Operation: 37+16=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37+95=132, Resulting Numbers: [79, 132], Heuristic score : (|79-55| + |132-55|)/2 = (24 + 77)/2 = 50.50\n\nGenerated Node #0,0,3: 55:[79, 132], Operation: 37+95=132\nExploring Operation: 132-79=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37+79=116, Resulting Numbers: [95, 116], Heuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\n\nGenerated Node #0,0,4: 55:[95, 116], Operation: 37+79=116\nExploring Operation: 116-95=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95+79=174, Resulting Numbers: [37, 174], Heuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\n\nGenerated Node #0,0,5: 55:[37, 174], Operation: 95+79=174\nExploring Operation: 174-37=137, Resulting Numbers: [137], \n137,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37*79=2923, Resulting Numbers: [95, 2923], Heuristic score : (|95-55| + |2923-55|)/2 = (40 + 2868)/2 = 1454.00\n\nGenerated Node #0,0,6: 55:[95, 2923], Operation: 37*79=2923\nExploring Operation: 2923-95=2828, Resulting Numbers: [2828], \n2828,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37*95=3515, Resulting Numbers: [79, 3515], Heuristic score : (|79-55| + |3515-55|)/2 = (24 + 3460)/2 = 1742.00\n\nGenerated Node #0,0,7: 55:[79, 3515], Operation: 37*95=3515\nExploring Operation: 3515-79=3436, Resulting Numbers: [3436], \n3436,55 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95*79=7505, Resulting Numbers: [37, 7505], Heuristic score : (|37-55| + |7505-55|)/2 = (18 + 7450)/2 = 3734.00\n\nGenerated Node #0,0,8: 55:[37, 7505], Operation: 95*79=7505\nExploring Operation: 7505-37=7468, Resulting Numbers: [7468], \n7468,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 11+37=48, Resulting Numbers: [90, 95, 48], Heuristic score : (|90-55| + |95-55| + |48-55|)/3 = (35 + 40 + 7)/3 = 27.33\n\nGenerated Node #0,1: 55:[90, 95, 48], Operation: 11+37=48\nExploring Operation: 95-48=47, Resulting Numbers: [90, 47], Heuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\n\nGenerated Node #0,1,0: 55:[90, 47], Operation: 95-48=47\nExploring Operation: 90-47=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90-48=42, Resulting Numbers: [95, 42], Heuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\n\nGenerated Node #0,1,1: 55:[95, 42], Operation: 90-48=42\nExploring Operation: 95-42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95-90=5, Resulting Numbers: [48, 5], Heuristic score : (|48-55| + |5-55|)/2 = (7 + 50)/2 = 28.50\n\nGenerated Node #0,1,2: 55:[48, 5], Operation: 95-90=5\nExploring Operation: 48+5=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90+48=138, Resulting Numbers: [95, 138], Heuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\n\nGenerated Node #0,1,3: 55:[95, 138], Operation: 90+48=138\nExploring Operation: 138-95=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95+48=143, Resulting Numbers: [90, 143], Heuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\n\nGenerated Node #0,1,4: 55:[90, 143], Operation: 95+48=143\nExploring Operation: 143-90=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90+95=185, Resulting Numbers: [48, 185], Heuristic score : (|48-55| + |185-55|)/2 = (7 + 130)/2 = 68.50\n\nGenerated Node #0,1,5: 55:[48, 185], Operation: 90+95=185\nExploring Operation: 185-48=137, Resulting Numbers: [137], \n137,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90*48=4320, Resulting Numbers: [95, 4320], Heuristic score : (|95-55| + |4320-55|)/2 = (40 + 4265)/2 = 2152.50\n\nGenerated Node #0,1,6: 55:[95, 4320], Operation: 90*48=4320\nExploring Operation: 4320-95=4225, Resulting Numbers: [4225], \n4225,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95*48=4560, Resulting Numbers: [90, 4560], Heuristic score : (|90-55| + |4560-55|)/2 = (35 + 4505)/2 = 2270.00\n\nGenerated Node #0,1,7: 55:[90, 4560], Operation: 95*48=4560\nExploring Operation: 4560-90=4470, Resulting Numbers: [4470], \n4470,55 unequal: No Solution\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90*95=8550, Resulting Numbers: [48, 8550], Heuristic score : (|48-55| + |8550-55|)/2 = (7 + 8495)/2 = 4251.00\n\nGenerated Node #0,1,8: 55:[48, 8550], Operation: 90*95=8550\nExploring Operation: 8550-48=8502, Resulting Numbers: [8502], \n8502,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-11=84, Resulting Numbers: [90, 37, 84], Heuristic score : (|90-55| + |37-55| + |84-55|)/3 = (35 + 18 + 29)/3 = 27.33\n\nGenerated Node #0,2: 55:[90, 37, 84], Operation: 95-11=84\nExploring Operation: 90-37=53, Resulting Numbers: [84, 53], Heuristic score : (|84-55| + |53-55|)/2 = (29 + 2)/2 = 15.50\n\nGenerated Node #0,2,0: 55:[84, 53], Operation: 90-37=53\nExploring Operation: 84-53=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 84-37=47, Resulting Numbers: [90, 47], Heuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\n\nGenerated Node #0,2,1: 55:[90, 47], Operation: 84-37=47\nExploring Operation: 90-47=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90-84=6, Resulting Numbers: [37, 6], Heuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\n\nGenerated Node #0,2,2: 55:[37, 6], Operation: 90-84=6\nExploring Operation: 37+6=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90+37=127, Resulting Numbers: [84, 127], Heuristic score : (|84-55| + |127-55|)/2 = (29 + 72)/2 = 50.50\n\nGenerated Node #0,2,3: 55:[84, 127], Operation: 90+37=127\nExploring Operation: 127-84=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 37+84=121, Resulting Numbers: [90, 121], Heuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\n\nGenerated Node #0,2,4: 55:[90, 121], Operation: 37+84=121\nExploring Operation: 121-90=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90+84=174, Resulting Numbers: [37, 174], Heuristic score : (|37-55| + |174-55|)/2 = (18 + 119)/2 = 68.50\n\nGenerated Node #0,2,5: 55:[37, 174], Operation: 90+84=174\nExploring Operation: 174-37=137, Resulting Numbers: [137], \n137,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 37*84=3108, Resulting Numbers: [90, 3108], Heuristic score : (|90-55| + |3108-55|)/2 = (35 + 3053)/2 = 1544.00\n\nGenerated Node #0,2,6: 55:[90, 3108], Operation: 37*84=3108\nExploring Operation: 3108-90=3018, Resulting Numbers: [3018], \n3018,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90*37=3330, Resulting Numbers: [84, 3330], Heuristic score : (|84-55| + |3330-55|)/2 = (29 + 3275)/2 = 1652.00\n\nGenerated Node #0,2,7: 55:[84, 3330], Operation: 90*37=3330\nExploring Operation: 3330-84=3246, Resulting Numbers: [3246], \n3246,55 unequal: No Solution\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90*84=7560, Resulting Numbers: [37, 7560], Heuristic score : (|37-55| + |7560-55|)/2 = (18 + 7505)/2 = 3761.50\n\nGenerated Node #0,2,8: 55:[37, 7560], Operation: 90*84=7560\nExploring Operation: 7560-37=7523, Resulting Numbers: [7523], \n7523,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-37=58, Resulting Numbers: [90, 11, 58], Heuristic score : (|90-55| + |11-55| + |58-55|)/3 = (35 + 44 + 3)/3 = 27.33\n\nGenerated Node #0,3: 55:[90, 11, 58], Operation: 95-37=58\nExploring Operation: 90-11=79, Resulting Numbers: [58, 79], Heuristic score : (|58-55| + |79-55|)/2 = (3 + 24)/2 = 13.50\n\nGenerated Node #0,3,0: 55:[58, 79], Operation: 90-11=79\nExploring Operation: 79-58=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 58-11=47, Resulting Numbers: [90, 47], Heuristic score : (|90-55| + |47-55|)/2 = (35 + 8)/2 = 21.50\n\nGenerated Node #0,3,1: 55:[90, 47], Operation: 58-11=47\nExploring Operation: 90-47=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90+11=101, Resulting Numbers: [58, 101], Heuristic score : (|58-55| + |101-55|)/2 = (3 + 46)/2 = 24.50\n\nGenerated Node #0,3,2: 55:[58, 101], Operation: 90+11=101\nExploring Operation: 101-58=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 11+58=69, Resulting Numbers: [90, 69], Heuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\n\nGenerated Node #0,3,3: 55:[90, 69], Operation: 11+58=69\nExploring Operation: 90-69=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90-58=32, Resulting Numbers: [11, 32], Heuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\n\nGenerated Node #0,3,4: 55:[11, 32], Operation: 90-58=32\nExploring Operation: 11+32=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90+58=148, Resulting Numbers: [11, 148], Heuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\n\nGenerated Node #0,3,5: 55:[11, 148], Operation: 90+58=148\nExploring Operation: 148-11=137, Resulting Numbers: [137], \n137,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 11*58=638, Resulting Numbers: [90, 638], Heuristic score : (|90-55| + |638-55|)/2 = (35 + 583)/2 = 309.00\n\nGenerated Node #0,3,6: 55:[90, 638], Operation: 11*58=638\nExploring Operation: 638-90=548, Resulting Numbers: [548], \n548,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90*11=990, Resulting Numbers: [58, 990], Heuristic score : (|58-55| + |990-55|)/2 = (3 + 935)/2 = 469.00\n\nGenerated Node #0,3,7: 55:[58, 990], Operation: 90*11=990\nExploring Operation: 990-58=932, Resulting Numbers: [932], \n932,55 unequal: No Solution\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90*58=5220, Resulting Numbers: [11, 5220], Heuristic score : (|11-55| + |5220-55|)/2 = (44 + 5165)/2 = 2604.50\n\nGenerated Node #0,3,8: 55:[11, 5220], Operation: 90*58=5220\nExploring Operation: 5220-11=5209, Resulting Numbers: [5209], \n5209,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90-37=53, Resulting Numbers: [11, 95, 53], Heuristic score : (|11-55| + |95-55| + |53-55|)/3 = (44 + 40 + 2)/3 = 28.67\n\nGenerated Node #0,4: 55:[11, 95, 53], Operation: 90-37=53\nExploring Operation: 95-11=84, Resulting Numbers: [53, 84], Heuristic score : (|53-55| + |84-55|)/2 = (2 + 29)/2 = 15.50\n\nGenerated Node #0,4,0: 55:[53, 84], Operation: 95-11=84\nExploring Operation: 84-53=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11+53=64, Resulting Numbers: [95, 64], Heuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\n\nGenerated Node #0,4,1: 55:[95, 64], Operation: 11+53=64\nExploring Operation: 95-64=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11+95=106, Resulting Numbers: [53, 106], Heuristic score : (|53-55| + |106-55|)/2 = (2 + 51)/2 = 26.50\n\nGenerated Node #0,4,2: 55:[53, 106], Operation: 11+95=106\nExploring Operation: 106-53=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 53-11=42, Resulting Numbers: [95, 42], Heuristic score : (|95-55| + |42-55|)/2 = (40 + 13)/2 = 26.50\n\nGenerated Node #0,4,3: 55:[95, 42], Operation: 53-11=42\nExploring Operation: 95-42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95-53=42, Resulting Numbers: [11, 42], Heuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\n\nGenerated Node #0,4,4: 55:[11, 42], Operation: 95-53=42\nExploring Operation: 11+42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95+53=148, Resulting Numbers: [11, 148], Heuristic score : (|11-55| + |148-55|)/2 = (44 + 93)/2 = 68.50\n\nGenerated Node #0,4,5: 55:[11, 148], Operation: 95+53=148\nExploring Operation: 148-11=137, Resulting Numbers: [137], \n137,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11*53=583, Resulting Numbers: [95, 583], Heuristic score : (|95-55| + |583-55|)/2 = (40 + 528)/2 = 284.00\n\nGenerated Node #0,4,6: 55:[95, 583], Operation: 11*53=583\nExploring Operation: 583-95=488, Resulting Numbers: [488], \n488,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11*95=1045, Resulting Numbers: [53, 1045], Heuristic score : (|53-55| + |1045-55|)/2 = (2 + 990)/2 = 496.00\n\nGenerated Node #0,4,7: 55:[53, 1045], Operation: 11*95=1045\nExploring Operation: 1045-53=992, Resulting Numbers: [992], \n992,55 unequal: No Solution\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95*53=5035, Resulting Numbers: [11, 5035], Heuristic score : (|11-55| + |5035-55|)/2 = (44 + 4980)/2 = 2512.00\n\nGenerated Node #0,4,8: 55:[11, 5035], Operation: 95*53=5035\nExploring Operation: 5035-11=5024, Resulting Numbers: [5024], \n5024,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+11=101, Resulting Numbers: [37, 95, 101], Heuristic score : (|37-55| + |95-55| + |101-55|)/3 = (18 + 40 + 46)/3 = 34.67\n\nGenerated Node #0,5: 55:[37, 95, 101], Operation: 90+11=101\nExploring Operation: 95-37=58, Resulting Numbers: [101, 58], Heuristic score : (|101-55| + |58-55|)/2 = (46 + 3)/2 = 24.50\n\nGenerated Node #0,5,0: 55:[101, 58], Operation: 95-37=58\nExploring Operation: 101-58=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 101-37=64, Resulting Numbers: [95, 64], Heuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\n\nGenerated Node #0,5,1: 55:[95, 64], Operation: 101-37=64\nExploring Operation: 95-64=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 101-95=6, Resulting Numbers: [37, 6], Heuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\n\nGenerated Node #0,5,2: 55:[37, 6], Operation: 101-95=6\nExploring Operation: 37+6=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37+95=132, Resulting Numbers: [101, 132], Heuristic score : (|101-55| + |132-55|)/2 = (46 + 77)/2 = 61.50\n\nGenerated Node #0,5,3: 55:[101, 132], Operation: 37+95=132\nExploring Operation: 132-101=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37+101=138, Resulting Numbers: [95, 138], Heuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\n\nGenerated Node #0,5,4: 55:[95, 138], Operation: 37+101=138\nExploring Operation: 138-95=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 95+101=196, Resulting Numbers: [37, 196], Heuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\n\nGenerated Node #0,5,5: 55:[37, 196], Operation: 95+101=196\nExploring Operation: 196-37=159, Resulting Numbers: [159], \n159,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37*95=3515, Resulting Numbers: [101, 3515], Heuristic score : (|101-55| + |3515-55|)/2 = (46 + 3460)/2 = 1753.00\n\nGenerated Node #0,5,6: 55:[101, 3515], Operation: 37*95=3515\nExploring Operation: 3515-101=3414, Resulting Numbers: [3414], \n3414,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37*101=3737, Resulting Numbers: [95, 3737], Heuristic score : (|95-55| + |3737-55|)/2 = (40 + 3682)/2 = 1861.00\n\nGenerated Node #0,5,7: 55:[95, 3737], Operation: 37*101=3737\nExploring Operation: 3737-95=3642, Resulting Numbers: [3642], \n3642,55 unequal: No Solution\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 95*101=9595, Resulting Numbers: [37, 9595], Heuristic score : (|37-55| + |9595-55|)/2 = (18 + 9540)/2 = 4779.00\n\nGenerated Node #0,5,8: 55:[37, 9595], Operation: 95*101=9595\nExploring Operation: 9595-37=9558, Resulting Numbers: [9558], \n9558,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 37-11=26, Resulting Numbers: [90, 95, 26], Heuristic score : (|90-55| + |95-55| + |26-55|)/3 = (35 + 40 + 29)/3 = 34.67\n\nGenerated Node #0,6: 55:[90, 95, 26], Operation: 37-11=26\nExploring Operation: 90-26=64, Resulting Numbers: [95, 64], Heuristic score : (|95-55| + |64-55|)/2 = (40 + 9)/2 = 24.50\n\nGenerated Node #0,6,0: 55:[95, 64], Operation: 90-26=64\nExploring Operation: 95-64=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95-26=69, Resulting Numbers: [90, 69], Heuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\n\nGenerated Node #0,6,1: 55:[90, 69], Operation: 95-26=69\nExploring Operation: 90-69=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95-90=5, Resulting Numbers: [26, 5], Heuristic score : (|26-55| + |5-55|)/2 = (29 + 50)/2 = 39.50\n\nGenerated Node #0,6,2: 55:[26, 5], Operation: 95-90=5\nExploring Operation: 26+5=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90+26=116, Resulting Numbers: [95, 116], Heuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\n\nGenerated Node #0,6,3: 55:[95, 116], Operation: 90+26=116\nExploring Operation: 116-95=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95+26=121, Resulting Numbers: [90, 121], Heuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\n\nGenerated Node #0,6,4: 55:[90, 121], Operation: 95+26=121\nExploring Operation: 121-90=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90+95=185, Resulting Numbers: [26, 185], Heuristic score : (|26-55| + |185-55|)/2 = (29 + 130)/2 = 79.50\n\nGenerated Node #0,6,5: 55:[26, 185], Operation: 90+95=185\nExploring Operation: 185-26=159, Resulting Numbers: [159], \n159,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90*26=2340, Resulting Numbers: [95, 2340], Heuristic score : (|95-55| + |2340-55|)/2 = (40 + 2285)/2 = 1162.50\n\nGenerated Node #0,6,6: 55:[95, 2340], Operation: 90*26=2340\nExploring Operation: 2340-95=2245, Resulting Numbers: [2245], \n2245,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95*26=2470, Resulting Numbers: [90, 2470], Heuristic score : (|90-55| + |2470-55|)/2 = (35 + 2415)/2 = 1225.00\n\nGenerated Node #0,6,7: 55:[90, 2470], Operation: 95*26=2470\nExploring Operation: 2470-90=2380, Resulting Numbers: [2380], \n2380,55 unequal: No Solution\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90*95=8550, Resulting Numbers: [26, 8550], Heuristic score : (|26-55| + |8550-55|)/2 = (29 + 8495)/2 = 4262.00\n\nGenerated Node #0,6,8: 55:[26, 8550], Operation: 90*95=8550\nExploring Operation: 8550-26=8524, Resulting Numbers: [8524], \n8524,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 11+95=106, Resulting Numbers: [90, 37, 106], Heuristic score : (|90-55| + |37-55| + |106-55|)/3 = (35 + 18 + 51)/3 = 34.67\n\nGenerated Node #0,7: 55:[90, 37, 106], Operation: 11+95=106\nExploring Operation: 106-37=69, Resulting Numbers: [90, 69], Heuristic score : (|90-55| + |69-55|)/2 = (35 + 14)/2 = 24.50\n\nGenerated Node #0,7,0: 55:[90, 69], Operation: 106-37=69\nExploring Operation: 90-69=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90-37=53, Resulting Numbers: [106, 53], Heuristic score : (|106-55| + |53-55|)/2 = (51 + 2)/2 = 26.50\n\nGenerated Node #0,7,1: 55:[106, 53], Operation: 90-37=53\nExploring Operation: 106-53=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 106-90=16, Resulting Numbers: [37, 16], Heuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\n\nGenerated Node #0,7,2: 55:[37, 16], Operation: 106-90=16\nExploring Operation: 37+16=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90+37=127, Resulting Numbers: [106, 127], Heuristic score : (|106-55| + |127-55|)/2 = (51 + 72)/2 = 61.50\n\nGenerated Node #0,7,3: 55:[106, 127], Operation: 90+37=127\nExploring Operation: 127-106=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 37+106=143, Resulting Numbers: [90, 143], Heuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\n\nGenerated Node #0,7,4: 55:[90, 143], Operation: 37+106=143\nExploring Operation: 143-90=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90+106=196, Resulting Numbers: [37, 196], Heuristic score : (|37-55| + |196-55|)/2 = (18 + 141)/2 = 79.50\n\nGenerated Node #0,7,5: 55:[37, 196], Operation: 90+106=196\nExploring Operation: 196-37=159, Resulting Numbers: [159], \n159,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90*37=3330, Resulting Numbers: [106, 3330], Heuristic score : (|106-55| + |3330-55|)/2 = (51 + 3275)/2 = 1663.00\n\nGenerated Node #0,7,6: 55:[106, 3330], Operation: 90*37=3330\nExploring Operation: 3330-106=3224, Resulting Numbers: [3224], \n3224,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 37*106=3922, Resulting Numbers: [90, 3922], Heuristic score : (|90-55| + |3922-55|)/2 = (35 + 3867)/2 = 1951.00\n\nGenerated Node #0,7,7: 55:[90, 3922], Operation: 37*106=3922\nExploring Operation: 3922-90=3832, Resulting Numbers: [3832], \n3832,55 unequal: No Solution\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90*106=9540, Resulting Numbers: [37, 9540], Heuristic score : (|37-55| + |9540-55|)/2 = (18 + 9485)/2 = 4751.50\n\nGenerated Node #0,7,8: 55:[37, 9540], Operation: 90*106=9540\nExploring Operation: 9540-37=9503, Resulting Numbers: [9503], \n9503,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-90=5, Resulting Numbers: [11, 37, 5], Heuristic score : (|11-55| + |37-55| + |5-55|)/3 = (44 + 18 + 50)/3 = 37.33\n\nGenerated Node #0,8: 55:[11, 37, 5], Operation: 95-90=5\nExploring Operation: 11*5=55, Resulting Numbers: [37, 55], Heuristic score : (|37-55| + |55-55|)/2 = (18 + 0)/2 = 9.00\n\nGenerated Node #0,8,0: 55:[37, 55], Operation: 11*5=55\nExploring Operation: 37+55=92, Resulting Numbers: [92], \n92,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11+37=48, Resulting Numbers: [5, 48], Heuristic score : (|5-55| + |48-55|)/2 = (50 + 7)/2 = 28.50\n\nGenerated Node #0,8,1: 55:[5, 48], Operation: 11+37=48\nExploring Operation: 5+48=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11+5=16, Resulting Numbers: [37, 16], Heuristic score : (|37-55| + |16-55|)/2 = (18 + 39)/2 = 28.50\n\nGenerated Node #0,8,2: 55:[37, 16], Operation: 11+5=16\nExploring Operation: 37+16=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37+5=42, Resulting Numbers: [11, 42], Heuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\n\nGenerated Node #0,8,3: 55:[11, 42], Operation: 37+5=42\nExploring Operation: 11+42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11-5=6, Resulting Numbers: [37, 6], Heuristic score : (|37-55| + |6-55|)/2 = (18 + 49)/2 = 33.50\n\nGenerated Node #0,8,4: 55:[37, 6], Operation: 11-5=6\nExploring Operation: 37+6=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37-5=32, Resulting Numbers: [11, 32], Heuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\n\nGenerated Node #0,8,5: 55:[11, 32], Operation: 37-5=32\nExploring Operation: 11+32=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37-11=26, Resulting Numbers: [5, 26], Heuristic score : (|5-55| + |26-55|)/2 = (50 + 29)/2 = 39.50\n\nGenerated Node #0,8,6: 55:[5, 26], Operation: 37-11=26\nExploring Operation: 5+26=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37*5=185, Resulting Numbers: [11, 185], Heuristic score : (|11-55| + |185-55|)/2 = (44 + 130)/2 = 87.00\n\nGenerated Node #0,8,7: 55:[11, 185], Operation: 37*5=185\nExploring Operation: 185-11=174, Resulting Numbers: [174], \n174,55 unequal: No Solution\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11*37=407, Resulting Numbers: [5, 407], Heuristic score : (|5-55| + |407-55|)/2 = (50 + 352)/2 = 201.00\n\nGenerated Node #0,8,8: 55:[5, 407], Operation: 11*37=407\nExploring Operation: 407-5=402, Resulting Numbers: [402], \n402,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+37=127, Resulting Numbers: [11, 95, 127], Heuristic score : (|11-55| + |95-55| + |127-55|)/3 = (44 + 40 + 72)/3 = 52.00\n\nGenerated Node #0,9: 55:[11, 95, 127], Operation: 90+37=127\nExploring Operation: 127-95=32, Resulting Numbers: [11, 32], Heuristic score : (|11-55| + |32-55|)/2 = (44 + 23)/2 = 33.50\n\nGenerated Node #0,9,0: 55:[11, 32], Operation: 127-95=32\nExploring Operation: 11+32=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95-11=84, Resulting Numbers: [127, 84], Heuristic score : (|127-55| + |84-55|)/2 = (72 + 29)/2 = 50.50\n\nGenerated Node #0,9,1: 55:[127, 84], Operation: 95-11=84\nExploring Operation: 127-84=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 127-11=116, Resulting Numbers: [95, 116], Heuristic score : (|95-55| + |116-55|)/2 = (40 + 61)/2 = 50.50\n\nGenerated Node #0,9,2: 55:[95, 116], Operation: 127-11=116\nExploring Operation: 116-95=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11+95=106, Resulting Numbers: [127, 106], Heuristic score : (|127-55| + |106-55|)/2 = (72 + 51)/2 = 61.50\n\nGenerated Node #0,9,3: 55:[127, 106], Operation: 11+95=106\nExploring Operation: 127-106=21, Resulting Numbers: [21], \n21,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11+127=138, Resulting Numbers: [95, 138], Heuristic score : (|95-55| + |138-55|)/2 = (40 + 83)/2 = 61.50\n\nGenerated Node #0,9,4: 55:[95, 138], Operation: 11+127=138\nExploring Operation: 138-95=43, Resulting Numbers: [43], \n43,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95+127=222, Resulting Numbers: [11, 222], Heuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\n\nGenerated Node #0,9,5: 55:[11, 222], Operation: 95+127=222\nExploring Operation: 222-11=211, Resulting Numbers: [211], \n211,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11*95=1045, Resulting Numbers: [127, 1045], Heuristic score : (|127-55| + |1045-55|)/2 = (72 + 990)/2 = 531.00\n\nGenerated Node #0,9,6: 55:[127, 1045], Operation: 11*95=1045\nExploring Operation: 1045-127=918, Resulting Numbers: [918], \n918,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11*127=1397, Resulting Numbers: [95, 1397], Heuristic score : (|95-55| + |1397-55|)/2 = (40 + 1342)/2 = 691.00\n\nGenerated Node #0,9,7: 55:[95, 1397], Operation: 11*127=1397\nExploring Operation: 1397-95=1302, Resulting Numbers: [1302], \n1302,55 unequal: No Solution\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95*127=12065, Resulting Numbers: [11, 12065], Heuristic score : (|11-55| + |12065-55|)/2 = (44 + 12010)/2 = 6027.00\n\nGenerated Node #0,9,8: 55:[11, 12065], Operation: 95*127=12065\nExploring Operation: 12065-11=12054, Resulting Numbers: [12054], \n12054,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 37+95=132, Resulting Numbers: [90, 11, 132], Heuristic score : (|90-55| + |11-55| + |132-55|)/3 = (35 + 44 + 77)/3 = 52.00\n\nGenerated Node #0,10: 55:[90, 11, 132], Operation: 37+95=132\nExploring Operation: 132-90=42, Resulting Numbers: [11, 42], Heuristic score : (|11-55| + |42-55|)/2 = (44 + 13)/2 = 28.50\n\nGenerated Node #0,10,0: 55:[11, 42], Operation: 132-90=42\nExploring Operation: 11+42=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 132/11=12, Resulting Numbers: [90, 12], Heuristic score : (|90-55| + |12-55|)/2 = (35 + 43)/2 = 39.00\n\nGenerated Node #0,10,1: 55:[90, 12], Operation: 132/11=12\nExploring Operation: 90-12=78, Resulting Numbers: [78], \n78,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90-11=79, Resulting Numbers: [132, 79], Heuristic score : (|132-55| + |79-55|)/2 = (77 + 24)/2 = 50.50\n\nGenerated Node #0,10,2: 55:[132, 79], Operation: 90-11=79\nExploring Operation: 132-79=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 132-11=121, Resulting Numbers: [90, 121], Heuristic score : (|90-55| + |121-55|)/2 = (35 + 66)/2 = 50.50\n\nGenerated Node #0,10,3: 55:[90, 121], Operation: 132-11=121\nExploring Operation: 121-90=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90+11=101, Resulting Numbers: [132, 101], Heuristic score : (|132-55| + |101-55|)/2 = (77 + 46)/2 = 61.50\n\nGenerated Node #0,10,4: 55:[132, 101], Operation: 90+11=101\nExploring Operation: 132-101=31, Resulting Numbers: [31], \n31,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 11+132=143, Resulting Numbers: [90, 143], Heuristic score : (|90-55| + |143-55|)/2 = (35 + 88)/2 = 61.50\n\nGenerated Node #0,10,5: 55:[90, 143], Operation: 11+132=143\nExploring Operation: 143-90=53, Resulting Numbers: [53], \n53,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90+132=222, Resulting Numbers: [11, 222], Heuristic score : (|11-55| + |222-55|)/2 = (44 + 167)/2 = 105.50\n\nGenerated Node #0,10,6: 55:[11, 222], Operation: 90+132=222\nExploring Operation: 222-11=211, Resulting Numbers: [211], \n211,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90*11=990, Resulting Numbers: [132, 990], Heuristic score : (|132-55| + |990-55|)/2 = (77 + 935)/2 = 506.00\n\nGenerated Node #0,10,7: 55:[132, 990], Operation: 90*11=990\nExploring Operation: 990-132=858, Resulting Numbers: [858], \n858,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 11*132=1452, Resulting Numbers: [90, 1452], Heuristic score : (|90-55| + |1452-55|)/2 = (35 + 1397)/2 = 716.00\n\nGenerated Node #0,10,8: 55:[90, 1452], Operation: 11*132=1452\nExploring Operation: 1452-90=1362, Resulting Numbers: [1362], \n1362,55 unequal: No Solution\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90*132=11880, Resulting Numbers: [11, 11880], Heuristic score : (|11-55| + |11880-55|)/2 = (44 + 11825)/2 = 5934.50\n\nGenerated Node #0,10,9: 55:[11, 11880], Operation: 90*132=11880\nExploring Operation: 11880/11=1080, Resulting Numbers: [1080], \n1080,55 unequal: No Solution\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+95=185, Resulting Numbers: [11, 37, 185], Heuristic score : (|11-55| + |37-55| + |185-55|)/3 = (44 + 18 + 130)/3 = 64.00\n\nGenerated Node #0,11: 55:[11, 37, 185], Operation: 90+95=185\nExploring Operation: 185/37=5, Resulting Numbers: [11, 5], Heuristic score : (|11-55| + |5-55|)/2 = (44 + 50)/2 = 47.00\n\nGenerated Node #0,11,0: 55:[11, 5], Operation: 185/37=5\nExploring Operation: 11*5=55, Resulting Numbers: [55], \n55,55 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['90+95=185', '185/37=5', '11*5=55']\nRESULT: 55\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Current State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90-11=79, Resulting Numbers: [37, 95, 79]\nGenerated Node #0,0: 55:[37, 95, 79] Operation: 90-11=79\nExploring Operation: 95-37=58, Resulting Numbers: [79, 58]\nGenerated Node #0,0,0: 55:[79, 58] Operation: 95-37=58\nExploring Operation: 79-58=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 79-37=42, Resulting Numbers: [95, 42]\nGenerated Node #0,0,1: 55:[95, 42] Operation: 79-37=42\nExploring Operation: 95-42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95-79=16, Resulting Numbers: [37, 16]\nGenerated Node #0,0,2: 55:[37, 16] Operation: 95-79=16\nExploring Operation: 37+16=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37+95=132, Resulting Numbers: [79, 132]\nGenerated Node #0,0,3: 55:[79, 132] Operation: 37+95=132\nExploring Operation: 132-79=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37+79=116, Resulting Numbers: [95, 116]\nGenerated Node #0,0,4: 55:[95, 116] Operation: 37+79=116\nExploring Operation: 116-95=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95+79=174, Resulting Numbers: [37, 174]\nGenerated Node #0,0,5: 55:[37, 174] Operation: 95+79=174\nExploring Operation: 174-37=137, Resulting Numbers: [137]\n137,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37*79=2923, Resulting Numbers: [95, 2923]\nGenerated Node #0,0,6: 55:[95, 2923] Operation: 37*79=2923\nExploring Operation: 2923-95=2828, Resulting Numbers: [2828]\n2828,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 37*95=3515, Resulting Numbers: [79, 3515]\nGenerated Node #0,0,7: 55:[79, 3515] Operation: 37*95=3515\nExploring Operation: 3515-79=3436, Resulting Numbers: [3436]\n3436,55 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 55:[37, 95, 79], Operations: ['90-11=79']\nExploring Operation: 95*79=7505, Resulting Numbers: [37, 7505]\nGenerated Node #0,0,8: 55:[37, 7505] Operation: 95*79=7505\nExploring Operation: 7505-37=7468, Resulting Numbers: [7468]\n7468,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 11+37=48, Resulting Numbers: [90, 95, 48]\nGenerated Node #0,1: 55:[90, 95, 48] Operation: 11+37=48\nExploring Operation: 95-48=47, Resulting Numbers: [90, 47]\nGenerated Node #0,1,0: 55:[90, 47] Operation: 95-48=47\nExploring Operation: 90-47=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90-48=42, Resulting Numbers: [95, 42]\nGenerated Node #0,1,1: 55:[95, 42] Operation: 90-48=42\nExploring Operation: 95-42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95-90=5, Resulting Numbers: [48, 5]\nGenerated Node #0,1,2: 55:[48, 5] Operation: 95-90=5\nExploring Operation: 48+5=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90+48=138, Resulting Numbers: [95, 138]\nGenerated Node #0,1,3: 55:[95, 138] Operation: 90+48=138\nExploring Operation: 138-95=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95+48=143, Resulting Numbers: [90, 143]\nGenerated Node #0,1,4: 55:[90, 143] Operation: 95+48=143\nExploring Operation: 143-90=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90+95=185, Resulting Numbers: [48, 185]\nGenerated Node #0,1,5: 55:[48, 185] Operation: 90+95=185\nExploring Operation: 185-48=137, Resulting Numbers: [137]\n137,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90*48=4320, Resulting Numbers: [95, 4320]\nGenerated Node #0,1,6: 55:[95, 4320] Operation: 90*48=4320\nExploring Operation: 4320-95=4225, Resulting Numbers: [4225]\n4225,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 95*48=4560, Resulting Numbers: [90, 4560]\nGenerated Node #0,1,7: 55:[90, 4560] Operation: 95*48=4560\nExploring Operation: 4560-90=4470, Resulting Numbers: [4470]\n4470,55 unequal: No Solution\n\nMoving to Node #0,1\nCurrent State: 55:[90, 95, 48], Operations: ['11+37=48']\nExploring Operation: 90*95=8550, Resulting Numbers: [48, 8550]\nGenerated Node #0,1,8: 55:[48, 8550] Operation: 90*95=8550\nExploring Operation: 8550-48=8502, Resulting Numbers: [8502]\n8502,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-11=84, Resulting Numbers: [90, 37, 84]\nGenerated Node #0,2: 55:[90, 37, 84] Operation: 95-11=84\nExploring Operation: 90-37=53, Resulting Numbers: [84, 53]\nGenerated Node #0,2,0: 55:[84, 53] Operation: 90-37=53\nExploring Operation: 84-53=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 84-37=47, Resulting Numbers: [90, 47]\nGenerated Node #0,2,1: 55:[90, 47] Operation: 84-37=47\nExploring Operation: 90-47=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90-84=6, Resulting Numbers: [37, 6]\nGenerated Node #0,2,2: 55:[37, 6] Operation: 90-84=6\nExploring Operation: 37+6=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90+37=127, Resulting Numbers: [84, 127]\nGenerated Node #0,2,3: 55:[84, 127] Operation: 90+37=127\nExploring Operation: 127-84=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 37+84=121, Resulting Numbers: [90, 121]\nGenerated Node #0,2,4: 55:[90, 121] Operation: 37+84=121\nExploring Operation: 121-90=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90+84=174, Resulting Numbers: [37, 174]\nGenerated Node #0,2,5: 55:[37, 174] Operation: 90+84=174\nExploring Operation: 174-37=137, Resulting Numbers: [137]\n137,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 37*84=3108, Resulting Numbers: [90, 3108]\nGenerated Node #0,2,6: 55:[90, 3108] Operation: 37*84=3108\nExploring Operation: 3108-90=3018, Resulting Numbers: [3018]\n3018,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90*37=3330, Resulting Numbers: [84, 3330]\nGenerated Node #0,2,7: 55:[84, 3330] Operation: 90*37=3330\nExploring Operation: 3330-84=3246, Resulting Numbers: [3246]\n3246,55 unequal: No Solution\n\nMoving to Node #0,2\nCurrent State: 55:[90, 37, 84], Operations: ['95-11=84']\nExploring Operation: 90*84=7560, Resulting Numbers: [37, 7560]\nGenerated Node #0,2,8: 55:[37, 7560] Operation: 90*84=7560\nExploring Operation: 7560-37=7523, Resulting Numbers: [7523]\n7523,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-37=58, Resulting Numbers: [90, 11, 58]\nGenerated Node #0,3: 55:[90, 11, 58] Operation: 95-37=58\nExploring Operation: 90-11=79, Resulting Numbers: [58, 79]\nGenerated Node #0,3,0: 55:[58, 79] Operation: 90-11=79\nExploring Operation: 79-58=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 58-11=47, Resulting Numbers: [90, 47]\nGenerated Node #0,3,1: 55:[90, 47] Operation: 58-11=47\nExploring Operation: 90-47=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90+11=101, Resulting Numbers: [58, 101]\nGenerated Node #0,3,2: 55:[58, 101] Operation: 90+11=101\nExploring Operation: 101-58=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 11+58=69, Resulting Numbers: [90, 69]\nGenerated Node #0,3,3: 55:[90, 69] Operation: 11+58=69\nExploring Operation: 90-69=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90-58=32, Resulting Numbers: [11, 32]\nGenerated Node #0,3,4: 55:[11, 32] Operation: 90-58=32\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90+58=148, Resulting Numbers: [11, 148]\nGenerated Node #0,3,5: 55:[11, 148] Operation: 90+58=148\nExploring Operation: 148-11=137, Resulting Numbers: [137]\n137,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 11*58=638, Resulting Numbers: [90, 638]\nGenerated Node #0,3,6: 55:[90, 638] Operation: 11*58=638\nExploring Operation: 638-90=548, Resulting Numbers: [548]\n548,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90*11=990, Resulting Numbers: [58, 990]\nGenerated Node #0,3,7: 55:[58, 990] Operation: 90*11=990\nExploring Operation: 990-58=932, Resulting Numbers: [932]\n932,55 unequal: No Solution\n\nMoving to Node #0,3\nCurrent State: 55:[90, 11, 58], Operations: ['95-37=58']\nExploring Operation: 90*58=5220, Resulting Numbers: [11, 5220]\nGenerated Node #0,3,8: 55:[11, 5220] Operation: 90*58=5220\nExploring Operation: 5220-11=5209, Resulting Numbers: [5209]\n5209,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90-37=53, Resulting Numbers: [11, 95, 53]\nGenerated Node #0,4: 55:[11, 95, 53] Operation: 90-37=53\nExploring Operation: 95-11=84, Resulting Numbers: [53, 84]\nGenerated Node #0,4,0: 55:[53, 84] Operation: 95-11=84\nExploring Operation: 84-53=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11+53=64, Resulting Numbers: [95, 64]\nGenerated Node #0,4,1: 55:[95, 64] Operation: 11+53=64\nExploring Operation: 95-64=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11+95=106, Resulting Numbers: [53, 106]\nGenerated Node #0,4,2: 55:[53, 106] Operation: 11+95=106\nExploring Operation: 106-53=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 53-11=42, Resulting Numbers: [95, 42]\nGenerated Node #0,4,3: 55:[95, 42] Operation: 53-11=42\nExploring Operation: 95-42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95-53=42, Resulting Numbers: [11, 42]\nGenerated Node #0,4,4: 55:[11, 42] Operation: 95-53=42\nExploring Operation: 11+42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95+53=148, Resulting Numbers: [11, 148]\nGenerated Node #0,4,5: 55:[11, 148] Operation: 95+53=148\nExploring Operation: 148-11=137, Resulting Numbers: [137]\n137,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11*53=583, Resulting Numbers: [95, 583]\nGenerated Node #0,4,6: 55:[95, 583] Operation: 11*53=583\nExploring Operation: 583-95=488, Resulting Numbers: [488]\n488,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 11*95=1045, Resulting Numbers: [53, 1045]\nGenerated Node #0,4,7: 55:[53, 1045] Operation: 11*95=1045\nExploring Operation: 1045-53=992, Resulting Numbers: [992]\n992,55 unequal: No Solution\n\nMoving to Node #0,4\nCurrent State: 55:[11, 95, 53], Operations: ['90-37=53']\nExploring Operation: 95*53=5035, Resulting Numbers: [11, 5035]\nGenerated Node #0,4,8: 55:[11, 5035] Operation: 95*53=5035\nExploring Operation: 5035-11=5024, Resulting Numbers: [5024]\n5024,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+11=101, Resulting Numbers: [37, 95, 101]\nGenerated Node #0,5: 55:[37, 95, 101] Operation: 90+11=101\nExploring Operation: 95-37=58, Resulting Numbers: [101, 58]\nGenerated Node #0,5,0: 55:[101, 58] Operation: 95-37=58\nExploring Operation: 101-58=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 101-37=64, Resulting Numbers: [95, 64]\nGenerated Node #0,5,1: 55:[95, 64] Operation: 101-37=64\nExploring Operation: 95-64=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 101-95=6, Resulting Numbers: [37, 6]\nGenerated Node #0,5,2: 55:[37, 6] Operation: 101-95=6\nExploring Operation: 37+6=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37+95=132, Resulting Numbers: [101, 132]\nGenerated Node #0,5,3: 55:[101, 132] Operation: 37+95=132\nExploring Operation: 132-101=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37+101=138, Resulting Numbers: [95, 138]\nGenerated Node #0,5,4: 55:[95, 138] Operation: 37+101=138\nExploring Operation: 138-95=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 95+101=196, Resulting Numbers: [37, 196]\nGenerated Node #0,5,5: 55:[37, 196] Operation: 95+101=196\nExploring Operation: 196-37=159, Resulting Numbers: [159]\n159,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37*95=3515, Resulting Numbers: [101, 3515]\nGenerated Node #0,5,6: 55:[101, 3515] Operation: 37*95=3515\nExploring Operation: 3515-101=3414, Resulting Numbers: [3414]\n3414,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 37*101=3737, Resulting Numbers: [95, 3737]\nGenerated Node #0,5,7: 55:[95, 3737] Operation: 37*101=3737\nExploring Operation: 3737-95=3642, Resulting Numbers: [3642]\n3642,55 unequal: No Solution\n\nMoving to Node #0,5\nCurrent State: 55:[37, 95, 101], Operations: ['90+11=101']\nExploring Operation: 95*101=9595, Resulting Numbers: [37, 9595]\nGenerated Node #0,5,8: 55:[37, 9595] Operation: 95*101=9595\nExploring Operation: 9595-37=9558, Resulting Numbers: [9558]\n9558,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 37-11=26, Resulting Numbers: [90, 95, 26]\nGenerated Node #0,6: 55:[90, 95, 26] Operation: 37-11=26\nExploring Operation: 90-26=64, Resulting Numbers: [95, 64]\nGenerated Node #0,6,0: 55:[95, 64] Operation: 90-26=64\nExploring Operation: 95-64=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95-26=69, Resulting Numbers: [90, 69]\nGenerated Node #0,6,1: 55:[90, 69] Operation: 95-26=69\nExploring Operation: 90-69=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95-90=5, Resulting Numbers: [26, 5]\nGenerated Node #0,6,2: 55:[26, 5] Operation: 95-90=5\nExploring Operation: 26+5=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90+26=116, Resulting Numbers: [95, 116]\nGenerated Node #0,6,3: 55:[95, 116] Operation: 90+26=116\nExploring Operation: 116-95=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95+26=121, Resulting Numbers: [90, 121]\nGenerated Node #0,6,4: 55:[90, 121] Operation: 95+26=121\nExploring Operation: 121-90=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90+95=185, Resulting Numbers: [26, 185]\nGenerated Node #0,6,5: 55:[26, 185] Operation: 90+95=185\nExploring Operation: 185-26=159, Resulting Numbers: [159]\n159,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90*26=2340, Resulting Numbers: [95, 2340]\nGenerated Node #0,6,6: 55:[95, 2340] Operation: 90*26=2340\nExploring Operation: 2340-95=2245, Resulting Numbers: [2245]\n2245,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 95*26=2470, Resulting Numbers: [90, 2470]\nGenerated Node #0,6,7: 55:[90, 2470] Operation: 95*26=2470\nExploring Operation: 2470-90=2380, Resulting Numbers: [2380]\n2380,55 unequal: No Solution\n\nMoving to Node #0,6\nCurrent State: 55:[90, 95, 26], Operations: ['37-11=26']\nExploring Operation: 90*95=8550, Resulting Numbers: [26, 8550]\nGenerated Node #0,6,8: 55:[26, 8550] Operation: 90*95=8550\nExploring Operation: 8550-26=8524, Resulting Numbers: [8524]\n8524,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 11+95=106, Resulting Numbers: [90, 37, 106]\nGenerated Node #0,7: 55:[90, 37, 106] Operation: 11+95=106\nExploring Operation: 106-37=69, Resulting Numbers: [90, 69]\nGenerated Node #0,7,0: 55:[90, 69] Operation: 106-37=69\nExploring Operation: 90-69=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90-37=53, Resulting Numbers: [106, 53]\nGenerated Node #0,7,1: 55:[106, 53] Operation: 90-37=53\nExploring Operation: 106-53=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 106-90=16, Resulting Numbers: [37, 16]\nGenerated Node #0,7,2: 55:[37, 16] Operation: 106-90=16\nExploring Operation: 37+16=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90+37=127, Resulting Numbers: [106, 127]\nGenerated Node #0,7,3: 55:[106, 127] Operation: 90+37=127\nExploring Operation: 127-106=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 37+106=143, Resulting Numbers: [90, 143]\nGenerated Node #0,7,4: 55:[90, 143] Operation: 37+106=143\nExploring Operation: 143-90=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90+106=196, Resulting Numbers: [37, 196]\nGenerated Node #0,7,5: 55:[37, 196] Operation: 90+106=196\nExploring Operation: 196-37=159, Resulting Numbers: [159]\n159,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90*37=3330, Resulting Numbers: [106, 3330]\nGenerated Node #0,7,6: 55:[106, 3330] Operation: 90*37=3330\nExploring Operation: 3330-106=3224, Resulting Numbers: [3224]\n3224,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 37*106=3922, Resulting Numbers: [90, 3922]\nGenerated Node #0,7,7: 55:[90, 3922] Operation: 37*106=3922\nExploring Operation: 3922-90=3832, Resulting Numbers: [3832]\n3832,55 unequal: No Solution\n\nMoving to Node #0,7\nCurrent State: 55:[90, 37, 106], Operations: ['11+95=106']\nExploring Operation: 90*106=9540, Resulting Numbers: [37, 9540]\nGenerated Node #0,7,8: 55:[37, 9540] Operation: 90*106=9540\nExploring Operation: 9540-37=9503, Resulting Numbers: [9503]\n9503,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 95-90=5, Resulting Numbers: [11, 37, 5]\nGenerated Node #0,8: 55:[11, 37, 5] Operation: 95-90=5\nExploring Operation: 11*5=55, Resulting Numbers: [37, 55]\nGenerated Node #0,8,0: 55:[37, 55] Operation: 11*5=55\nExploring Operation: 37+55=92, Resulting Numbers: [92]\n92,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11+37=48, Resulting Numbers: [5, 48]\nGenerated Node #0,8,1: 55:[5, 48] Operation: 11+37=48\nExploring Operation: 5+48=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11+5=16, Resulting Numbers: [37, 16]\nGenerated Node #0,8,2: 55:[37, 16] Operation: 11+5=16\nExploring Operation: 37+16=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37+5=42, Resulting Numbers: [11, 42]\nGenerated Node #0,8,3: 55:[11, 42] Operation: 37+5=42\nExploring Operation: 11+42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11-5=6, Resulting Numbers: [37, 6]\nGenerated Node #0,8,4: 55:[37, 6] Operation: 11-5=6\nExploring Operation: 37+6=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37-5=32, Resulting Numbers: [11, 32]\nGenerated Node #0,8,5: 55:[11, 32] Operation: 37-5=32\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37-11=26, Resulting Numbers: [5, 26]\nGenerated Node #0,8,6: 55:[5, 26] Operation: 37-11=26\nExploring Operation: 5+26=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 37*5=185, Resulting Numbers: [11, 185]\nGenerated Node #0,8,7: 55:[11, 185] Operation: 37*5=185\nExploring Operation: 185-11=174, Resulting Numbers: [174]\n174,55 unequal: No Solution\n\nMoving to Node #0,8\nCurrent State: 55:[11, 37, 5], Operations: ['95-90=5']\nExploring Operation: 11*37=407, Resulting Numbers: [5, 407]\nGenerated Node #0,8,8: 55:[5, 407] Operation: 11*37=407\nExploring Operation: 407-5=402, Resulting Numbers: [402]\n402,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+37=127, Resulting Numbers: [11, 95, 127]\nGenerated Node #0,9: 55:[11, 95, 127] Operation: 90+37=127\nExploring Operation: 127-95=32, Resulting Numbers: [11, 32]\nGenerated Node #0,9,0: 55:[11, 32] Operation: 127-95=32\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95-11=84, Resulting Numbers: [127, 84]\nGenerated Node #0,9,1: 55:[127, 84] Operation: 95-11=84\nExploring Operation: 127-84=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 127-11=116, Resulting Numbers: [95, 116]\nGenerated Node #0,9,2: 55:[95, 116] Operation: 127-11=116\nExploring Operation: 116-95=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11+95=106, Resulting Numbers: [127, 106]\nGenerated Node #0,9,3: 55:[127, 106] Operation: 11+95=106\nExploring Operation: 127-106=21, Resulting Numbers: [21]\n21,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11+127=138, Resulting Numbers: [95, 138]\nGenerated Node #0,9,4: 55:[95, 138] Operation: 11+127=138\nExploring Operation: 138-95=43, Resulting Numbers: [43]\n43,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95+127=222, Resulting Numbers: [11, 222]\nGenerated Node #0,9,5: 55:[11, 222] Operation: 95+127=222\nExploring Operation: 222-11=211, Resulting Numbers: [211]\n211,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11*95=1045, Resulting Numbers: [127, 1045]\nGenerated Node #0,9,6: 55:[127, 1045] Operation: 11*95=1045\nExploring Operation: 1045-127=918, Resulting Numbers: [918]\n918,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 11*127=1397, Resulting Numbers: [95, 1397]\nGenerated Node #0,9,7: 55:[95, 1397] Operation: 11*127=1397\nExploring Operation: 1397-95=1302, Resulting Numbers: [1302]\n1302,55 unequal: No Solution\n\nMoving to Node #0,9\nCurrent State: 55:[11, 95, 127], Operations: ['90+37=127']\nExploring Operation: 95*127=12065, Resulting Numbers: [11, 12065]\nGenerated Node #0,9,8: 55:[11, 12065] Operation: 95*127=12065\nExploring Operation: 12065-11=12054, Resulting Numbers: [12054]\n12054,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 37+95=132, Resulting Numbers: [90, 11, 132]\nGenerated Node #0,10: 55:[90, 11, 132] Operation: 37+95=132\nExploring Operation: 132-90=42, Resulting Numbers: [11, 42]\nGenerated Node #0,10,0: 55:[11, 42] Operation: 132-90=42\nExploring Operation: 11+42=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 132/11=12, Resulting Numbers: [90, 12]\nGenerated Node #0,10,1: 55:[90, 12] Operation: 132/11=12\nExploring Operation: 90-12=78, Resulting Numbers: [78]\n78,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90-11=79, Resulting Numbers: [132, 79]\nGenerated Node #0,10,2: 55:[132, 79] Operation: 90-11=79\nExploring Operation: 132-79=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 132-11=121, Resulting Numbers: [90, 121]\nGenerated Node #0,10,3: 55:[90, 121] Operation: 132-11=121\nExploring Operation: 121-90=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90+11=101, Resulting Numbers: [132, 101]\nGenerated Node #0,10,4: 55:[132, 101] Operation: 90+11=101\nExploring Operation: 132-101=31, Resulting Numbers: [31]\n31,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 11+132=143, Resulting Numbers: [90, 143]\nGenerated Node #0,10,5: 55:[90, 143] Operation: 11+132=143\nExploring Operation: 143-90=53, Resulting Numbers: [53]\n53,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90+132=222, Resulting Numbers: [11, 222]\nGenerated Node #0,10,6: 55:[11, 222] Operation: 90+132=222\nExploring Operation: 222-11=211, Resulting Numbers: [211]\n211,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90*11=990, Resulting Numbers: [132, 990]\nGenerated Node #0,10,7: 55:[132, 990] Operation: 90*11=990\nExploring Operation: 990-132=858, Resulting Numbers: [858]\n858,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 11*132=1452, Resulting Numbers: [90, 1452]\nGenerated Node #0,10,8: 55:[90, 1452] Operation: 11*132=1452\nExploring Operation: 1452-90=1362, Resulting Numbers: [1362]\n1362,55 unequal: No Solution\n\nMoving to Node #0,10\nCurrent State: 55:[90, 11, 132], Operations: ['37+95=132']\nExploring Operation: 90*132=11880, Resulting Numbers: [11, 11880]\nGenerated Node #0,10,9: 55:[11, 11880] Operation: 90*132=11880\nExploring Operation: 11880/11=1080, Resulting Numbers: [1080]\n1080,55 unequal: No Solution\n\nMoving to Node #0\nCurrent State: 55:[90, 11, 37, 95], Operations: []\nExploring Operation: 90+95=185, Resulting Numbers: [11, 37, 185]\nGenerated Node #0,11: 55:[11, 37, 185] Operation: 90+95=185\nExploring Operation: 185/37=5, Resulting Numbers: [11, 5]\nGenerated Node #0,11,0: 55:[11, 5] Operation: 185/37=5\nExploring Operation: 11*5=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['90+95=185', '185/37=5', '11*5=55']\nRESULT: 55\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [90, 11, 37, 95] using only arithmetic operations (+, -, *, /) to reach the target value 55. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to combine the numbers 90, 11, 37, and 95 using only addition, subtraction, multiplication, and division to get exactly 55. All four numbers must be used exactly once. Hmm, let's see how I can approach this.\n\nFirst, I should list out all the numbers: 90, 11, 37, 95. I need to use each once. The target is 55, which is a bit tricky because the numbers are all quite large except for 11. Maybe I can start by looking for pairs that can be combined to get numbers that might help reach 55.\n\nLet me think about possible operations. Perhaps subtraction or division could help reduce the larger numbers. For example, 95 minus 90 is 5. That's a small number, but maybe useful. Or 90 divided by something? 90 divided by 11 is about 8.18, not sure if that helps. 37 divided by 11 is around 3.36. Not sure either.\n\nWait, maybe I can combine some operations step by step. Let's try starting with 95. If I subtract 90 from 95, that gives me 5. So 95-90=5. Now I have 5, 11, and 37 left. How can I combine these? Maybe 5 + 11 is 16, and then 16 + 37 is 53, which is close to 55 but not quite. Or 11 + 37 is 48, then 5 +48 is 53. Still 2 short.\n\nAlternatively, maybe I can multiply 5 by something. 5 multiplied by 11 is 55, but I still have 37 left. Oh wait, that's a problem because I have to use all four numbers. So if I do 5*11=55, I still have 37, which I haven't used yet. That doesn't work because I have to use each number exactly once.\n\nHmm, maybe I should try a different approach. Let's think about combining other pairs first. For instance, 90 and 37. If I subtract 37 from 90, that's 53. Then I have 95, 11, and 53. But 53 plus 11 is 64, which is way over 55. Or 53 multiplied by something? 53 is close to 55, but I don't see an easy way.\n\nWait, perhaps I should try division. If I take 95 divided by 11, that's approximately 8.636. Not sure. Or 90 divided by 37 is about 2.432. Maybe that's not helpful.\n\nAnother idea: maybe use multiplication on two numbers and then adjust with the others. For example, 11 multiplied by 5 is 55, but I need to get 5 from the other numbers. Let's see: 90, 37, 95. If I do 95 - 90, that's 5, as before. Then 5 * 11 is 55, but then I still have 37 unused. So that doesn't work.\n\nWait, maybe I can combine 37 and 11 first. 37 minus 11 is 26. Then I have 90 and 95 left. If I can combine 90 and 95 to get something that, when combined with 26, gives 55. Let's see: 90 + 95 is 185, which is way too big. 95 - 90 is 5. Then 5 and 26: 5 +26 is 31, which is too small. 26 -5 is 21, still no. 5*26 is 130, too big. 26/5 is 5.2, not helpful.\n\nAlternatively, 90 divided by 37 is about 2.432. If I have 2.432, then maybe combine it with 11. 2.432 + 11 is 13.432, which doesn't help. Or 11 - 2.432 is 8.568. Not useful either.\n\nWait, maybe I should try a different pair first. Let's try 37 and 95. 95 -37 is 58. Then I have 90 and 11 left. 58 is close to 55, but how can I adjust it? If I can subtract 3 from 58, I get 55. But 90 and 11: 90 -11 is 79, which is way too big. Or 11 - (90) is negative. Alternatively, maybe 90 divided by 11 is about 8.18. Then 58 -8.18 is about 49.8, which is not 55. Hmm.\n\nAlternatively, maybe I can do 90 +11=101. Then 101 and 37 and 95. Let's see: 101 -37=64, then 64 -95 is negative. Or 101 -95=6, then 6 +37=43, which is less than 55. Not helpful.\n\nWait, another approach: maybe use division to create a fraction that can be subtracted or added to get closer. For example, 90 divided by 11 is approximately 8.18. If I subtract that from something else# [omitted steps] Let's see, 37 minus 8.18 is about 28.82. Then 95 minus 28.82 is about 66.18, which is too big. Not helpful.\n\nAlternatively, maybe multiply two numbers and divide by another. For example, 90 * 11 = 990. Then divide by something. 990 divided by 37 is approximately 26.756. Then 26.756 and 95: 95 -26.756 is about 68.244, which is not 55. Alternatively, 990 divided by 95 is about 10.42. Then 10.42 + something? Not sure.\n\nAnother idea: perhaps 95 minus (90 + something). Let's see, 95 -90 is 5. Then if I can subtract 5 from something else, but that would require using 5 twice, which I can't do.\n\nWait, maybe I can do 95 - (90 + 11) = 95 -101 = -6. Then -6 and 37: -6 +37=31, which is still not 55. Alternatively, 37 - (-6)=43, which is closer but not 55.\n\nWait, perhaps I should consider more complex operations, like combining three numbers first and then the fourth. Let's try that. For example, (95 - 90) =5, then 5 +11=16, then 16 +37=53. So 53 is close to 55, but I'm missing 2. Hmm, but that uses all four numbers, but the result is 53, not 55. So that's not it.\n\nWait, maybe I can adjust the order. Let's try 95 - (90 - something). For example, 90 -37=53. Then 95 -53=42. Then 42 and 11: 42 +11=53, again, same result. Or 42 -11=31. Not helpful.\n\nAlternatively, 90 - (95 -37)= 90 -58=32. Then 32 +11=43, not 55.\n\nHmm, maybe I'm approaching this wrong. Let's think about factors of 55. 55 is 5*11, so maybe if I can get 5 and 11 and then multiply them. But I need to use 90 and 37 as well. Wait, how?\n\nIf I can get 5 from 95 -90=5, then 5 *11=55. But then I still have 37 left, which I haven't used. So that doesn't work because I have to use all four numbers. Unless I can incorporate 37 into the equation somehow.\n\nWait, maybe I can do something like (95 -90) * (37 -11). Let's calculate that: 5 *26=130. That's too big, but maybe I can divide it by something. 130 divided by 2 is 65, which is bigger than 55. Alternatively, 130 - something. But I don't have any numbers left because I've used all four. So that doesn't help.\n\nAlternatively, maybe I can do 95/(90 - (37 -11)). Let's compute the denominator: 37-11=26, then 90-26=64. So 95/64 is approximately 1.484. That's not helpful.\n\nWait, perhaps I can think of 55 as (90 + 11) - (95 -37). Let's see: 90+11=101, 95-37=58. Then 101-58=43. Not 55.\n\nAlternatively, 90 + (11 - (95/37)). Let's compute 95/37≈2.567. Then 11-2.567≈8.433. Then 90 +8.433≈98.433. Not 55.\n\nAnother idea: Maybe subtract a larger number from a smaller one and then adjust. For example, 11 - (95 -90)=11 -5=6. Then 6 +37=43, still not 55.\n\nWait, what if I do (95 - 37) * (90 /11). Let's compute 95-37=58, 90/11≈8.18. Then 58 *8.18≈474.4. Way too big.\n\nAlternatively, (95 -37) + (90 -11)=58 +79=137. Nope.\n\nHmm, this is tricky. Let me try a different approach. Maybe using division to reduce a number. For instance, 90 divided by 37 is about 2.432. Then 2.432 +11=13.432. Then 13.432 +95=108.432. Not helpful.\n\nWait, perhaps I can do 90 - (95 -37)=90-58=32. Then 32 +11=43. Still not 55.\n\nAlternatively, 95 - (90 -37)=95-53=42. Then 42 -11=31. Not helpful.\n\nWait, maybe I should try using multiplication and division together. Let's see, 90 *11=990. Then 990 divided by something. If I do 990/(37 + something). 37 + what? 37 + (95 -90)=37+5=42. Then 990/42≈23.571. Not helpful.\n\nAlternatively, 90/(11 + something). 11 +37=48. 90/48≈1.875. Then 1.875 *95≈178.125. Not helpful.\n\nWait, perhaps I can think of 55 as (95 - 90) * (37 -11). Wait, 95-90=5, 37-11=26. 5*26=130. That's too big, but maybe I can subtract something. 130 - (something). But I've already used all four numbers, so I can't use any more.\n\nAlternatively, maybe 55 = (90 - 37) + (95 -11). Let's compute: 90-37=53, 95-11=84. 53+84=137, which is way over.\n\nWait, another idea: Maybe (95 / (90 - (37 +11))). Let's compute the denominator: 37+11=48, 90-48=42. So 95/42≈2.2619. Not helpful.\n\nAlternatively, (95 - (90 +37)) *11. 95-127=-32. -32*11=-352. No.\n\nHmm, maybe I'm missing something. Let's try to think of 55 as a combination of two numbers first, and then see how to get the rest. 55 could be 95 -40, so if I can get 40 from 90, 11, 37. But 90 is too big, so maybe 90 - something. 90 -50=40, but I don't have 50. Alternatively, 11* something. 11*3.636≈40. Hmm, but I don't have that.\n\nAlternatively, 37 +3=40, but again, I don't have 3. Maybe 90 - (37 + something). 90-37=53, then 53 -13=40, but I don't have 13. Wait, 11 + something=13? 11+2=13, but I don't have 2.\n\nWait, maybe I can get 40 by doing (90 +11)/something. 90+11=101. 101 divided by something. 101/2.525≈40, but that's not helpful.\n\nAnother approach: Maybe I can use subtraction to get a negative number that can help. For example, 90 -95= -5. Then -5 +37=32, then 32 +11=43. Not 55.\n\nAlternatively, 95 -90=5, then 5 + (37 -11)=5+26=31. Still not.\n\nWait, maybe I can do 95 - (90 / (37 -11)). Let's compute 37-11=26. Then 90/26≈3.4615. Then 95 -3.4615≈91.538. Not helpful.\n\nHmm, this is getting frustrating. Let me try to list all possible operations step by step.\n\nFirst, pick two numbers and perform an operation. Let's start with 95 and 90.\n\nOption 1: 95 +90=185. Then I have 185, 11,37. Now, I need to combine these three to get 55. Hmm, 185 is way too big. Maybe subtract 185-11=174, then 174-37=137. No. Or 185-37=148, then 148-11=137. Still no.\n\nOption 2: 95 -90=5. Now I have 5,11,37. Need to combine these to get 55. Let's see:\n\n5 +11=16, then 16 +37=53. Close, but not 55.\n\n5 +11=16, 16 *37=592. Way too big.\n\n5 *11=55, but then 55 +37=92. No. Or 55 -37=18. Not helpful.\n\nAlternatively, 5 + (11 +37)=5+48=53. Still no.\n\nSo option 2 doesn't work.\n\nOption 3: 95 *90=8550. Too big. Not helpful.\n\nOption 4: 95 /90≈1.055. Then combine with 11 and 37. Not helpful.\n\nSo starting with 95 and 90 doesn't seem promising.\n\nLet's try starting with 95 and 37.\n\nOption 1: 95+37=132. Then have 132,90,11. Need to get 55.\n\n132 is too big. Maybe 132 -90=42, then 42 -11=31. Not 55.\n\nOr 132 -11=121, then 121 -90=31. Still no.\n\nOption 2: 95-37=58. Now have 58,90,11.\n\n58 +90=148, 148-11=137. No.\n\n58 -90=-32, -32 +11=-21. No.\n\nAlternatively, 58 +11=69, 69 +90=159. No.\n\nOption 3: 95*37=3519. Way too big.\n\nOption 4: 95/37≈2.567. Then have 2.567,90,11. Not helpful.\n\nSo starting with 95 and37 doesn't help.\n\nNext, try 95 and11.\n\nOption1:95+11=106. Then have 106,90,37.\n\n106 -90=16, 16 +37=53. Close but no.\n\n106 -37=69, 69 -90=-21. No.\n\nOption2:95-11=84. Then have 84,90,37.\n\n84 +90=174, 174-37=137. No.\n\n84 +37=121, 121 -90=31. No.\n\nOption3:95*11=1045. Too big.\n\nOption4:95/11≈8.636. Then have 8.636,90,37.\n\nNot useful.\n\nNow, let's try starting with 90 and37.\n\nOption1:90+37=127. Then have 127,95,11.\n\n127 is too big. 127-95=32, 32 -11=21. No.\n\nOption2:90-37=53. Then have 53,95,11.\n\n53 +95=148, 148-11=137. No.\n\n53 -95=-42, -42 +11=-31. No.\n\nOption3:90*37=3330. Too big.\n\nOption4:90/37≈2.432. Then have 2.432,95,11.\n\nNot helpful.\n\nNext, try starting with 90 and11.\n\nOption1:90+11=101. Then have 101,95,37.\n\n101 is big. 101-95=6, 6 +37=43. No.\n\nOption2:90-11=79. Then have 79,95,37.\n\n79 +95=174, 174-37=137. No.\n\n79 -95=-16, -16 +37=21. No.\n\nOption3:90*11=990. Too big.\n\nOption4:90/11≈8.18. Then have 8.18,95,37.\n\nNot helpful.\n\nLastly, try starting with 37 and11.\n\nOption1:37+11=48. Then have 48,90,95.\n\n48 +90=138, 138 -95=43. No.\n\n48 +95=143, 143 -90=53. Close but no.\n\nOption2:37-11=26. Then have 26,90,95.\n\n26 +90=116, 116 -95=21. No.\n\n26 -90=-64, -64 +95=31. No.\n\nOption3:37*11=407. Too big.\n\nOption4:37/11≈3.364. Then have 3.364,90,95.\n\nNot helpful.\n\nHmm, I'm stuck. Maybe I need to consider more complex operations, like combining three numbers first and then incorporating the fourth. Let's try that.\n\nFor example, take 95 - (90 +11) =95-101=-6. Then -6 +37=31. Not 55.\n\nAlternatively, (95 -90) + (37 -11)=5 +26=31. No.\n\nWait, maybe (95 / (90 - (37 -11))). Let's compute denominator:37-11=26, 90-26=64. So 95/64≈1.484. Not helpful.\n\nAnother idea: (90 - (95 -37)) *11. Compute inside:95-37=58, 90-58=32",
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] | null | true | 23,845 | true | 11,290 | true | 233 | false | 4,102 | false | 0 |
[
70,
63,
75,
32
] | 100 |
[
"70-63=7",
"75+32=107",
"107-7=100"
] | 0.993056 |
dfs
|
sum_heuristic
|
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Current State: 100:[70, 63, 75, 32], Operations: []\nExploring Operation: 70-63=7, Resulting Numbers: [75, 32, 7]\nGenerated Node #2: [75, 32, 7] from Operation: 70-63=7\nCurrent State: 100:[75, 32, 7], Operations: ['70-63=7']\nExploring Operation: 75+32=107, Resulting Numbers: [7, 107]\nGenerated Node #3: [7, 107] from Operation: 75+32=107\nCurrent State: 100:[7, 107], Operations: ['70-63=7', '75+32=107']\nExploring Operation: 107-7=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['70-63=7', '75+32=107', '107-7=100']\nRESULT: 100\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "We have these numbers [70, 63, 75, 32]. Our goal is to produce 100. Let's show the search process step by step:\nOne possible strategy is to use a Depth-First Search (DFS) guided by a **sum-based** heuristic, which computes the average of the absolute differences between each number and the target number.\nLower scores indicate that, on average, the numbers are closer to the target, making the state more promising for reaching the target via additive operations.\n\n\nCurrent State #0: 100:[70, 63, 75, 32]. Operations so far : [].\n\nThought : Expand Node #0’s 1st child to build next frontier.\nAction : Exploring operation 63+32=95. \nResulting numbers: [70, 75, 95].\nHeuristic score : (|70-100| + |75-100| + |95-100|)/3 = (30 + 25 + 5)/3 = 20.00\nGenerated Node #0,0: 100:[70, 75, 95] Operation: 63+32=95\n\nThought : Expand Node #0,0’s 1st child to build next frontier.\nAction : Exploring operation 70+75=145. \nResulting numbers: [95, 145].\nHeuristic score : (|95-100| + |145-100|)/2 = (5 + 45)/2 = 25.00\nGenerated Node #0,0,0: 100:[95, 145] Operation: 70+75=145\n\nThought : Expand Node #0,0,0’s 1st child to build next frontier.\nAction : Exploring operation 145-95=50. \nResulting numbers: [50].\n50,100 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 20.0\nCurrent State #0,0: 100:[70, 75, 95]. Operations so far : ['63+32=95'].\n\nThought : Expand Node #0,0’s 2nd child to build next frontier.\nAction : Exploring operation 70+95=165. \nResulting numbers: [75, 165].\nHeuristic score : (|75-100| + |165-100|)/2 = (25 + 65)/2 = 45.00\nGenerated Node #0,0,1: 100:[75, 165] Operation: 70+95=165\n\nThought : Expand Node #0,0,1’s 1st child to build next frontier.\nAction : Exploring operation 165-75=90. \nResulting numbers: [90].\n90,100 unequal: No Solution ... backtracking\n\nThought : Selecting next node to expand based on heuristic value\nAction : Moving to Node #0,0 with lowest heuristic value 20.0\nCurrent State #0,0: 100:[70, 75, 95]. Operations so far : ['63+32=95'].\n\nThought : Expand Node #0,0’s 3rd child to build next frontier.\nAction : Exploring operation 75-70=5. \nResulting numbers: [95, 5].\nHeuristic score : (|95-100| + |5-100|)/2 = (5 + 95)/2 = 50.00\nGenerated Node #0,0,2: 100:[95, 5] Operation: 75-70=5\n\nThought : Expand Node #0,0,2’s 1st child to build next frontier.\nAction : Exploring operation 95+5=100. \nResulting numbers: [100].\n100,100 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['63+32=95', '75-70=5', '95+5=100']\nRESULT: 100\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Current State: 100:[70, 63, 75, 32], Operations: []\nExploring Operation: 63+32=95, Resulting Numbers: [70, 75, 95], Heuristic score : (|70-100| + |75-100| + |95-100|)/3 = (30 + 25 + 5)/3 = 20.00\n\nGenerated Node #0,0: 100:[70, 75, 95], Operation: 63+32=95\nExploring Operation: 70+75=145, Resulting Numbers: [95, 145], Heuristic score : (|95-100| + |145-100|)/2 = (5 + 45)/2 = 25.00\n\nGenerated Node #0,0,0: 100:[95, 145], Operation: 70+75=145\nExploring Operation: 145-95=50, Resulting Numbers: [50], \n50,100 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 100:[70, 75, 95], Operations: ['63+32=95']\nExploring Operation: 70+95=165, Resulting Numbers: [75, 165], Heuristic score : (|75-100| + |165-100|)/2 = (25 + 65)/2 = 45.00\n\nGenerated Node #0,0,1: 100:[75, 165], Operation: 70+95=165\nExploring Operation: 165-75=90, Resulting Numbers: [90], \n90,100 unequal: No Solution\nMoving to Node #0,0\nCurrent State: 100:[70, 75, 95], Operations: ['63+32=95']\nExploring Operation: 75-70=5, Resulting Numbers: [95, 5], Heuristic score : (|95-100| + |5-100|)/2 = (5 + 95)/2 = 50.00\n\nGenerated Node #0,0,2: 100:[95, 5], Operation: 75-70=5\nExploring Operation: 95+5=100, Resulting Numbers: [100], \n100,100 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['63+32=95', '75-70=5', '95+5=100']\nRESULT: 100\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Current State: 100:[70, 63, 75, 32], Operations: []\nExploring Operation: 63+32=95, Resulting Numbers: [70, 75, 95]\nGenerated Node #0,0: 100:[70, 75, 95] Operation: 63+32=95\nExploring Operation: 70+75=145, Resulting Numbers: [95, 145]\nGenerated Node #0,0,0: 100:[95, 145] Operation: 70+75=145\nExploring Operation: 145-95=50, Resulting Numbers: [50]\n50,100 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 100:[70, 75, 95], Operations: ['63+32=95']\nExploring Operation: 70+95=165, Resulting Numbers: [75, 165]\nGenerated Node #0,0,1: 100:[75, 165] Operation: 70+95=165\nExploring Operation: 165-75=90, Resulting Numbers: [90]\n90,100 unequal: No Solution\n\nMoving to Node #0,0\nCurrent State: 100:[70, 75, 95], Operations: ['63+32=95']\nExploring Operation: 75-70=5, Resulting Numbers: [95, 5]\nGenerated Node #0,0,2: 100:[95, 5] Operation: 75-70=5\nExploring Operation: 95+5=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n\n```\nSOLUTION: YES\nOPERATIONS: ['63+32=95', '75-70=5', '95+5=100']\nRESULT: 100\n```\n",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
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{
"content": "<think>\nOkay, so I've got this problem where I need to combine the numbers 70, 63, 75, and 32 using only addition, subtraction, multiplication, or division. The goal is to reach exactly 100, and I have to use each number exactly once. Hmm, that sounds a bit tricky, but let's see how I can approach it.\n\nFirst, I think I should list out all the numbers: 70, 63, 75, 32. Maybe I can try different combinations to see which operations get me closer to 100. I remember that sometimes combining larger numbers first can help, but I'm not sure. Let me start by looking at the numbers and seeing which operations might be useful.\n\nI notice that 70 and 75 are both large numbers, so maybe adding them would get me somewhere. Let's try 70 + 75. That gives me 145. Hmm, that's way over 100. Maybe I can subtract something from that. But wait, I also have 63 and 32 left. Maybe I can subtract 63 and 32 from 145. Let's see: 145 - 63 = 82, then 82 - 32 = 50. That's too low. So that approach doesn't work.\n\nAlright, maybe I should try a different approach. What if I subtract 70 and 63 first? Let's see, 70 - 63 = 7. Then I have 7, 75, and 32 left. Hmm, 7 + 75 = 82, then 82 + 32 = 114. That's over 100. Maybe I can subtract instead. 7 * 75 would be 525, which is way too high. Maybe division? 75 / 7 is about 10.7, which doesn't seem helpful.\n\nWait, perhaps I should try combining 75 and 32 first. Let's see, 75 - 32 = 43. Now I have 70, 63, and 43. Maybe 70 + 63 = 133, which is too high. If I subtract 43 from that, 133 - 43 = 90. Close to 100, but not quite. Maybe I can adjust the operations.\n\nAnother idea: what if I multiply 70 and 32? 70 * 32 = 2240. That's way too big. Maybe divide instead. 70 / 32 is about 2.1875. Doesn't seem helpful.\n\nLet me try combining 63 and 32. 63 + 32 = 95. That's just 5 short of 100. Hmm, if I can add 5 somehow. But where would I get 5 from? I have 70 and 75 left. Maybe 75 - 70 = 5. Oh, that's a thought! So 75 - 70 = 5, and then 95 + 5 = 100. Wait, does that work?\n\nLet me check:\n\nFirst, combine 63 and 32: 63 + 32 = 95.\n\nThen, combine 75 and 70: 75 - 70 = 5.\n\nThen, add those two results: 95 + 5 = 100.\n\nSo the operations would be:\n\n63 + 32 = 95\n\n75 - 70 = 5\n\n95 + 5 = 100\n\nThat seems to use each number exactly once and only uses addition and subtraction. Let me make sure I didn't miss anything.\n\nWait, but does the order matter? Let me see. I used 63 and 32 first, then 75 and 70, and then combined the two results. That should be valid. Each number is used once, and each operation is a single arithmetic step.\n\nSo the operations list would be:\n\n['63+32=95', '75-70=5', '95+5=100']\n\nAnd the result is 100. So the solution is possible.\n</think>\n\nSOLUTION: YES\nOPERATIONS: ['63+32=95', '75-70=5', '95+5=100']\nRESULT: 100",
"role": "assistant"
}
] |
[
{
"content": "Combine these initial numbers [70, 63, 75, 32] using only arithmetic operations (+, -, *, /) to reach the target value 100. All initial numbers must be used exactly once.\nConclude with the final result in EXACTLY this format:\n```\nSOLUTION: YES/NO\nOPERATIONS: list of string of operations performed, each string involving only 1 operation. For example, ['A+B=C','C+D=E'] is allowed, ['A+B+D=E'] is not allowed\nRESULT: final_value\n```\n",
"role": "user"
},
{
"content": "Okay, let's see. I need to combine the numbers 70, 63, 75, and 32 using each exactly once with arithmetic operations to get 100. All right, let's start thinking.\n\nFirst, maybe I should try to see if adding or subtracting some of them can get close. Let's look at the numbers. 70 and 63 are both in the 60-70 range. 75 is a bit higher, and 32 is lower. Maybe subtract some of the bigger numbers and use the smaller ones to adjust?\n\nLet me try different combinations. Let's think about possible pairs. For example, if I add 70 and 32, that gives 102. Then maybe subtract something. Wait, 70 +32 =102. Then maybe 102 minus (something) equals 100. But 102-2=100. Where can I get 2 from? The remaining numbers are 63 and 75. Hmm, 75-63=12. Not helpful. Or maybe 63-75= -12. Hmm. So 102 minus (75-63) would be 102 -12=90. Not enough.\n\nAlternatively, maybe 75 -32=43. Then add that to 70: 70+43=113. Then subtract 63? 113-63=50. No. That's not right.\n\nWait, maybe multiply. Let's see. 75 divided by something. 75 divided by 3 is 25. But how do I get 3 from the other numbers? Like 63 divided by 21=3? Not sure. Let's think differently.\n\nWhat if I take 75 and subtract 63? That gives 12. Then multiply by something. 12 multiplied by 8.333... would be 100. But how to get 8.333. Let's see. 70 and 32. Maybe 70 divided by 32? 70/32 is approximately 2.1875. Not helpful. Hmm.\n\nWait, maybe combine 70 and 63 first. 70 +63=133. Then subtract 75: 133-75=58. Then add 32: 58+32=90. Not 100. Not helpful. Another approach.\n\nWhat about multiplying two numbers? Like 70 * something. 70*1.428... would be 100. But how to get that. Let's see. 70*( (63+75)/32 )? Let's calculate (63+75)=138. 138/32 is 4.3125. 70 *4.3125=301.875. Not helpful.\n\nAlternatively, 70 multiplied by 63 is way too big. 70*63=4410. Divided by something. 4410 divided by 75 is 58.8. Then plus 32 would be 90.8. Still no.\n\nAnother idea: 75 - (32 / something). Let's see. 32 divided by something. If I do 32/(75-70), which is 32/5=6.4. Then subtract that from 63? 63-6.4=56.6. Not helpful.\n\nWait, maybe using division in a way that gives a higher number. Like 63 divided by something. For instance, 63/(0.75) is 84. Then add 70 and 32. 84 +70=154 +32=186. No.\n\nHmm. Let's try another angle. Let's think about how to get 100. Maybe 100 = (something * something) - (something else). For example, 75 * 1.333 (approx 100). But how to get 1.333 from other numbers. 70/(63-32) =70/31≈2.258. Not helpful.\n\nWait, 70 + (75 - (63 -32)). Let's compute that. 63-32=31. Then 75-31=44. Then 70+44=114. Not 100.\n\nAlternatively, (70 +75) - (63 +32). 145 -95=50. No.\n\nWhat if I subtract 32 from 75 first: 75-32=43. Then add that to 70: 70+43=113. Subtract 63: 113-63=50. Still not.\n\nWait, maybe multiply two numbers and then divide by another. Let's see. Suppose I do (70 * 75) = 5250. Then divide by 63? 5250/63=83.333... Then add 32? 83.333 +32=115.333. No.\n\nOr 70*63=4410. Divide by 75? 58.8. Then 58.8 +32=90.8. Still not.\n\nAlternatively, (75 * 63) =4725. Divide by 70? 67.5. Then 67.5 +32=99.5. Oh, close! That's 99.5. Just 0.5 short. Hmm. Wait, perhaps if I can adjust that. Maybe (75 * 63) divided by (70 - something). Let me think.\n\nWait, 75 multiplied by 32. Let's see. 75*32=2400. Divided by 63+70=133. 2400/133 ≈ 18.04. Not helpful.\n\nAlternatively, (63 + 75) =138. Multiply by 70? 138*70=9660. Divided by 32. 9660/32=301.875. No.\n\nWhat if I subtract 32 from 63? 63-32=31. Then 70 +31=101. Then add 75? 101+75=176. No. Not close.\n\nWait, maybe 70 divided by (something). Let's say 70 divided by 0.7. That's 100. How to get 0.7 from 63,75,32. Hmm. For example, 63 divided by (75+32) is 63/107≈0.589. Not 0.7. Alternatively, (75 -32) =43. 70/43 ≈1.627. Not helpful.\n\nAnother approach: let's try to get 100 as a combination of two numbers. For example, 100 = A + B, where A and B are results from combining two numbers each. Let's see. Let's say A is 70 + 63=133. Then B would need to be -33. But the remaining numbers are 75 and 32. 75-32=43. So 133 -43=90. No.\n\nAlternatively, 70 -63=7. Then 7 + (75 +32) = 7+107=114. Not 100.\n\nHmm. What if I do (70 - (75 / (63 -32))) ?\n\nCompute 63-32=31. Then 75 divided by 31≈2.419. Then 70 -2.419≈67.58. Then what's left? 63 and 32 have been used? Wait, no. Wait, let's track usage. Each number must be used exactly once. So perhaps:\n\nStep 1: 63-32=31 (using 63 and 32).\n\nStep 2: 75 / 31 ≈2.419 (using 75 and the result from step 1).\n\nThen step 3: 70 - that result. So 70 -2.419≈67.58. But then all numbers used? Wait, 70,75,63,32 are all used. Because 63 and 32 were used in step 1, 75 in step 2, 70 in step 3. So this gives 67.58, which isn't 100.\n\nNot helpful. Let's think again.\n\nWait, perhaps combining 70 and 32 first. Let's say 70+32=102. Then need to subtract 2 to get 100. How to get 2 from 63 and 75. Maybe 75 -63=12. Then 102 -12=90. No. Alternatively, 63 divided by something. 63 divided by 31.5 is 2. But how to get 31.5. Hmm. Wait, 63/(75-32)=63/43≈1.465. So 102 -1.465≈100.535. Close but not exact. But since all operations have to be exact, fractions would matter.\n\nWait, 75-32=43. Then 63 divided by 43 is (63/43). Then 102 - (63/43) = (102*43 -63)/43 = (4386 -63)/43=4323/43≈100.534. Not exactly 100. So no.\n\nHmm. Maybe another way. Let's try (70 + 63) =133. Then 75 -32=43. Then 133 -43=90. No.\n\nAlternatively, 70 * (something) =100. Let's see. 70 * (10/7) =100. How to get 10/7 from the remaining numbers. The remaining numbers are 63,75,32. So perhaps (75 -32) =43. Then 43 /63 = 43/63≈0.682. Not 10/7≈1.428. So that's not helpful.\n\nAnother idea: 63 multiplied by something. Let's say 63*(1.587)=100. How to get that multiplier. For example, (70 +32)/75. 70+32=102. 102/75=1.36. Then 63*1.36=85.68. Not 100.\n\nAlternatively, 63*(32/(75-70)). 75-70=5. 32/5=6.4. 63*6.4=403.2. Way too high.\n\nHmm. Let's think about division. Let's see. 75 divided by 3 is 25. 25*4=100. How to get 3 and 4 from the other numbers. Wait, 63 divided by (70 -32)=63/38≈1.657. Not 3. Alternatively, 63 -32=31. 70 divided by 31≈2.258. Not 4.\n\nAlternatively, maybe 70/(75 -63) =70/12≈5.833. Then multiply by 32. 5.833*32≈186.666. No.\n\nWait, let's think again. Let's try to get 100 as (something) times (something else). For example, 32 *3.125=100. How to get 3.125. 3.125 is 25/8. Hmm. Let's see. If I can get 25 from the other numbers and divide by 8. 70 - (63+75) =70-138= -68. Not helpful. Alternatively, 75 - (63 + something). Not sure.\n\nAlternatively, (70 + 63) =133. 75-32=43. 133 -43=90. Still not.\n\nWait, maybe a combination of multiplication and division. Let's see:\n\n(75 * 32) =2400. Then, 2400 divided by (something) =100. So 2400 / (something) =100 → something=24. So how can I make 24 from 70 and 63. 70-63=7. 70/63≈1.111. No. 63-70= -7. Not helpful. So (75*32)=2400 divided by (70-63)=7 →2400/7≈342.857. Not 100. Not helpful.\n\nAnother approach: 70 +63=133. Then 133 -75=58. 58 +32=90. Not helpful.\n\nAlternatively, (75 +63)=138. Then 138 -32=106. 106-70=36. No.\n\nHmm. Let's think of using division in a way that gives a larger number. For example, (75 / something) plus another number. 75 divided by 0.75 is 100. But how to get 0.75 from 70,63,32. Let's see. 63 divided by (70+32) =63/102≈0.617. Not 0.75. 32/(70+63)=32/133≈0.240. No.\n\nAlternatively, (70 +32)=102. 75/102≈0.735. Then 0.735*63≈46.305. Adding that to 75/102*63? Not sure. Maybe not helpful.\n\nWait, perhaps 63/(75-32) +70. Let's compute 75-32=43. 63/43≈1.465. 1.465+70=71.465. No.\n\nAnother idea: Let's use all four numbers with a mix of operations. For example, ((70 - 63) * (75 -32)). So 7 *43=301. Not 100.\n\nHmm. Maybe (70 * (32 - (75 -63))). Let's compute 75-63=12. 32-12=20. 70*20=1400. No. Too big.\n\nWait, 75 - (70 / (63 -32)) → 63-32=31. 70/31≈2.258. 75-2.258≈72.74. Then, what's left? The other numbers (70,63,32 have been used in steps?), but wait, the initial numbers must be used exactly once. So perhaps the operations have to combine them step by step, each step using two numbers or one number and an intermediate result. Let's think in terms of combining two at a time, then combining the result with the next.\n\nFor example, first combine 70 and 63: let's say 70 +63=133. Then combine 133 with 75: maybe 133-75=58. Then combine 58 with32: 58+32=90. No. Not 100.\n\nAlternatively, first combine 70 and 75. 70+75=145. Then combine 145 with 63: 145-63=82. Then 82 +32=114. No.\n\nOr 70*75=5250. Then 5250/63=83.333... Then 83.333+32=115.333. No.\n\nAnother approach: 75 +32=107. Then 107 - (70 -63)=107-7=100. Oh! Wait, that's possible. Let me check:\n\nYes! Let's see:\n\nFirst step: 75 +32 =107. \n\nSecond step: 70 -63=7. \n\nThird step: 107 -7=100. \n\nThat uses all numbers once. \n\nSo the operations would be:\n\n75 +32=107 (using 75 and 32), \n\n70-63=7 (using 70 and 63), \n\nthen 107 -7=100. \n\nSo the list of operations would be ['75+32=107', '70-63=7', '107-7=100'].\n\nYes, that seems to work. All numbers used exactly once. Let's verify the steps:\n\n75 +32 =107. \n\nThen 70-63=7. \n\nThen subtract those two results: 107-7=100. \n\nYes! That's correct. So the answer is yes, with these operations.\n```\nSOLUTION: YES\nOPERATIONS: ['75+32=107', '70-63=7', '107-7=100']\nRESULT: 100\n```",
"role": "assistant"
}
] | true | 862 | true | 390 | true | 224 | true | 868 | true | 3,362 |
[
5,
5,
33,
33
] | 76 |
[
"5+5=10",
"33+33=66",
"10+66=76"
] | 0.978299 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | [{"content":"Combine these initial numbers [5, 5, 33, 33] using only arithmetic operations (+, -, *,(...TRUNCATED) | true | 2,749 | true | 1,276 | true | 224 | true | 681 | true | 1,469 |
[
34,
19,
42,
7
] | 28 |
[
"34+42=76",
"76/19=4",
"7*4=28"
] | 0.795139 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [34, 19, 42, 7] using only arithmetic operations (+, -, *(...TRUNCATED) | true | 25,804 | true | 12,240 | true | 224 | false | 4,112 | true | 14,440 |
[
64,
50,
12,
56
] | 70 |
[
"64+50=114",
"56-12=44",
"114-44=70"
] | 0.993056 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [64, 50, 12, 56] using only arithmetic operations (+, -, (...TRUNCATED) | true | 870 | true | 390 | true | 224 | true | 720 | true | 2,468 |
[
86,
8,
22,
89
] | 58 |
[
"89-86=3",
"22*3=66",
"66-8=58"
] | 0 |
bfs_5
|
sum_heuristic
| [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [86, 8, 22, 89] using only arithmetic operations (+, -, *(...TRUNCATED) | false | 16,117 | false | 7,960 | true | 224 | true | 923 | true | 5,487 |
[
15,
63,
92,
77
] | 91 |
[
"15+63=78",
"92+77=169",
"169-78=91"
] | 0.993056 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [15, 63, 92, 77] using only arithmetic operations (+, -, (...TRUNCATED) | true | 870 | true | 390 | true | 224 | true | 1,822 | true | 727 |
[
37,
48,
26,
74
] | 50 |
[
"37*48=1776",
"1776/74=24",
"26+24=50"
] | 0.84375 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [37, 48, 26, 74] using only arithmetic operations (+, -, (...TRUNCATED) | null | true | 19,899 | true | 9,404 | true | 236 | false | 4,104 | false | 0 |
[
83,
23,
43,
84
] | 65 |
[
"83+23=106",
"84-43=41",
"106-41=65"
] | 0.946181 |
bfs_5
|
sum_heuristic
| [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | [{"content":"Combine these initial numbers [83, 23, 43, 84] using only arithmetic operations (+, -, (...TRUNCATED) | true | 6,232 | true | 2,929 | true | 224 | true | 783 | true | 976 |
[
20,
31,
9,
39
] | 88 |
[
"20-9=11",
"39-31=8",
"11*8=88"
] | 0.887153 |
dfs
|
sum_heuristic
| [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | [{"content":"Combine these initial numbers [20, 31, 9, 39] using only arithmetic operations (+, -, *(...TRUNCATED) | true | 14,142 | true | 6,748 | true | 224 | false | 4,100 | true | 5,195 |
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