conversation listlengths 2 2 | seed int64 65.7k 199M | task_id int64 2.15M 895M | task_metadata dict | task_type stringclasses 8
values | usage null |
|---|---|---|---|---|---|
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 31,709,960 | 831,709,960 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "()(([[[()()]]()]))()",
"error_indices": [
6,
7,
11,
20,
22
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_so... | dyck_language_reasoning_errors | null |
[
{
"content": "Numbers [5, 6, 8, 10], target value 100, operators ['+', '-', '*'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no s... | 37,716,444 | 137,716,444 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "en",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "Define ○, the rules are as follows:\non the real number field, x ○ y = abs(x ** x) + x - x - y.\nThe precedence of operations: ** > * = / = % = ○ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the exp... | 70,502,423 | 270,502,423 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "english",
"letter_words":... | operation | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 83,545,436 | 883,545,436 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]()[(())][]([[[]]][])()",
"error_indices": [
6,
7,
8,
9,
26
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_... | dyck_language_reasoning_errors | null |
[
{
"content": "Define ○, the rules are as follows:\non the real number field, x ○ y = (y * y - x).\nThe precedence of operations: ** > * = / = % > + = - = ○。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ○... | 10,209,415 | 210,209,415 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "8 ○ 8",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "english",
"letter_wor... | operation | null |
[
{
"content": "分析以下逻辑表达式：\n\nA. ((not (((1 - 0) < (10 * -19)) or (((17 % 3) == (16 - 7)) or (2024年奥运会在巴黎举办。)))) and (not (章鱼有8条腿。))) and (((((泰国位于非洲。) and (第一次世界大战开始发生在1914年。)) or (not ((9 * -3 * 3 * -2) != (-9 - -7)))) and ((50小于等于7。) and ((-2 + 6) != (-13 - 12))) and ((冰的密度比液态水小。) and (((-12 * -2) <= (-4 - 7))... | 2,788,459 | 602,788,459 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((not (((1 - 0) < (10 * -19)) or (((17 % 3) == (16 - 7)) or (2024年奥运会在巴黎举办。)))) and (not (章鱼有8条腿。))) and (((((泰国位于非洲。) and (第一次世界... | boolean_expressions | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: <[⟨⟩{}][{<>}<⟨⟩<([⟨⟩][(⟨{<>⟨[]⟩<<{<([⟨{<⟨<<\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is re... | 60,776,178 | 60,776,178 | {
"closing_sequence": ">>⟩>}⟩])>}>>}⟩)])>>]>",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 21,
"full_sequence": "<[⟨⟩{}][{<>}<⟨⟩<([⟨⟩][(⟨{<>⟨[]⟩<<{<([⟨{<⟨<<>>⟩>}⟩])>}>>}⟩)])>>]>",
"given... | dyck_language | null |
[
{
"content": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = x * x + abs(y + 3)。\n和 ▽，规则如下：\n实数域上，x ▽ y = x + y * y + x * x。\n和 ◎，规则如下：\n实数域上，x ◎ y = x * x / y + x / y。\n运算优先级：⊗ > ** = ◎ > * = / = % > + = - = ▽。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ⊗ 8 ▽ 4 ◎ 2\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "u... | 83,324,845 | 283,324,845 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "3 ⊗ 8 ▽ 4 ◎ 2",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"le... | operation | null |
[
{
"content": "数字 [1, 10, 14, 15]，想办法用 ['+', '-'] 得到 60。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\nNone```",
"reasoning_content": null,
"role": ... | 41,410,161 | 141,410,161 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": false,
"language": "zh",
"letter_words": nu... | game_of_24 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: {}]])>)})>})>]>]}]}))]\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid s... | 129,452,885 | 529,452,885 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "[(({[{[<[<({<({(<([[{}]])>)})>})>]>]}]}))]",
"given_count": null,
"is_solvable": null,
"... | dyck_language2 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ({⟦(⟦[⟨⟩⟦⦃[]<⟦⦃[[({<⦃[[<⟦{⟨⟦⟨\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProv... | 97,603,154 | 97,603,154 | {
"closing_sequence": "⟩⟧⟩}⟧>]]⦄>})]]⦄⟧>⦄⟧]⟧)⟧})",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 25,
"full_sequence": "({⟦(⟦[⟨⟩⟦⦃[]<⟦⦃[[({<⦃[[<⟦{⟨⟦⟨⟩⟧⟩}⟧>]]⦄>})]]⦄⟧>⦄⟧]⟧)⟧})",
"given_count... | dyck_language | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 69,599,361 | 869,599,361 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]()()()()[(()[])()]",
"error_indices": [
4,
9
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"langua... | dyck_language_reasoning_errors | null |
[
{
"content": "Solve the following Sudoku puzzle. Fill in the empty cells (marked with '.') with digits 1-9.\n\nRules:\n- Each row must contain digits 1-9 with no repetition\n- Each column must contain digits 1-9 with no repetition\n- Each 3x3 box must contain digits 1-9 with no repetition\n\nPuzzle:\n```\n7...4... | 29,197,893 | 729,197,893 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 29,
"is_solvable": null,
"language": "en",
"letter_words": n... | sudoku | null |
[
{
"content": "给你 [1, 4, 5, 8]，用 ['+', '-', '*', '/'] 算出 60。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n(1*8+4)*5```",
"reasoning_content": null,
... | 59,203,972 | 159,203,972 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "zh",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "定义 ◎，规则如下：\n当x和y的和是奇数时，x ◎ y = x * y * x * x；\n其他情况下，x ◎ y = x + y / 5 + x。\n和 ☆，规则如下：\n当x小于y时，x ☆ y = y ** y * x；\n其他情况下，x ☆ y = x - x / y - x。\n运算优先级：☆ > ** > * = / = % > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 9 % 6 ☆ 3 ◎ 5\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
... | 98,015,781 | 298,015,781 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "9 % 6 ☆ 3 ◎ 5",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"le... | operation | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ⟨⟩(⦃⦃<{⦃⦄⟨[<⟦⦃⟨{<>{<{⦃{<⦃⦄<[⟨⟩{<⟨<[<<<⟦⟨({({<<⟦<⟦(⦃⦃{⦃\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond... | 52,159,528 | 52,159,528 | {
"closing_sequence": "⦄}⦄⦄)⟧>⟧>>})})⟩⟧>>>]>⟩>}]>>}⦄}>}}⟩⦄⟧>]⟩}>⦄⦄)",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 44,
"full_sequence": "⟨⟩(⦃⦃<{⦃⦄⟨[<⟦⦃⟨{<>{<{⦃{<⦃⦄<[⟨⟩{<⟨<[<<<⟦⟨({({<<⟦<⟦(⦃⦃... | dyck_language | null |
[
{
"content": "Let S = \"⟧]]⟩)]}⦄]⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "```⟨... | 125,265,132 | 525,265,132 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 10,
"full_sequence": "⟨[⦃{[(⟨[[⟦⟧]]⟩)]}⦄]⟩",
"given_count": null,
"is_solvable": null,
"language": null,
"le... | dyck_language2 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ()⟨⟩⟦⟦⟨<>{⟦⟧<>}()⟩{}⟧⟨⟦<>⦃⦃⟦⟧⦃⦄(<(⦃()⦄)><()⟨{[<>⟦()⟧[⟦⟧{}](⟨[]⟩⟦⟧){⟦(<⦃⦃⦃⦃⦃{{⟨\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any ex... | 7,994,205 | 7,994,205 | {
"closing_sequence": "⟩}}⦄⦄⦄⦄⦄>)⟧}]}⟩>)⦄⦄⟧⟩⟧",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 22,
"full_sequence": "()⟨⟩⟦⟦⟨<>{⟦⟧<>}()⟩{}⟧⟨⟦<>⦃⦃⟦⟧⦃⦄(<(⦃()⦄)><()⟨{[<>⟦()⟧[⟦⟧{}](⟨[]⟩⟦⟧){⟦(<⦃⦃⦃⦃... | dyck_language | null |
[
{
"content": "In this alphametic puzzle: MBUXA + FAKMXX + UKAVBK = FKKXXFV, each letter represents a distinct digit from 0-9. Determine the digits that make the equation valid. Please end your response in the last line with the following format: The answer is $YOUR_ANSWER. $YOUR_ANSWER should be the equation wi... | 43,994,451 | 343,994,451 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": 6,
"B": 2,
"C": null,
"D": null,
"E": null,
"F": 1,
"G": null,
"H": null,
"I": null,
"J": null,
"K": 0,
"L": null,
"M": 4,
"N": null,
"O": null,
"P": null,
"Q": ... | cryptarithm | null |
[
{
"content": "下面是几个布尔表达式：\n\nA. (not (not (not (丹麦的货币是加元。)))) or (not ((not ((9 + -9) < (2 ** 2) < (3 ** 3))) or ((鹰是鸟类。) or ((0 * -5 + -7 * -2) > (-11 * -14)))))\nB. (((not (1900年奥运会在巴黎举办。)) and (not (以色列的货币是兰特。))) and ((((-1 * 14) >= (18 % 10)) and (酒精在常温下是液体。)) and ((光速比声速快。) and (钻石由碳元素组成。)))) or (墨西哥的首都是阿姆... | 97,244,213 | 697,244,213 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(not (not (not (丹麦的货币是加元。)))) or (not ((not ((9 + -9) < (2 ** 2) < (3 ** 3))) or ((鹰是鸟类。) or ((0 * -5 + -7 * -2) > (-11 * -14))))... | boolean_expressions | null |
[
{
"content": "Complete this Sudoku puzzle. Replace each '.' with a digit from 1 to 9.\n\n```\n.4....91.\n.72.....5\n1........\n........9\n.28...143\n.....4726\n214...6.8\n69.2....1\n..5....7.\n```\n\nRules: Each row, column, and 3x3 box must contain all digits 1-9 exactly once.\n\nOutput the solved grid in the ... | 86,087,734 | 786,087,734 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 28,
"is_solvable": null,
"language": "en",
"letter_words": n... | sudoku | null |
[
{
"content": "Define ♡, the rules are as follows:\nwhen y is odd, x ♡ y = (x + y - 2);\notherwise, x ♡ y = y / x - x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = x * 2 - y.\nThe precedence of operations: ♡ > ** > * = / = % > + = - = ♢。\nParentheses have the highest priority, and t... | 99,146,279 | 299,146,279 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "4 ♡ 1 / 10 ♢ 5 ♡ 1",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "english",
... | operation | null |
[
{
"content": "已知字母等式：CDC + CSW + CDDDS = CWSCS（其中CDC是3位数、CSW是3位数、CDDDS是5位数、CWSCS是5位数），每个字母代表一个数字，不同字母代表不同数字。请找出让等式成立的数字替换方案。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "909 + 981 + 90008 = 91898",
"reasoning_content... | 79,938,571 | 379,938,571 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": 9,
"D": 0,
"E": null,
"F": null,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": null,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not ((Carbon dioxide is a solid at room temperature.) or (There are 31 days in December.)))\nB. (not ((39 % 6) < (-9 - 1))) and (not not ((-3 * -19) <= (-16 + 7) <= (8 * -2 * -2 * 5))) and (not (((-1 + 0) > (-... | 63,864,331 | 663,864,331 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not (not ((Carbon dioxide is a solid at room temperature.) or (There are 31 days in December.)))",
"True"
],
[
... | boolean_expressions | null |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 12,047,947 | 812,047,947 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<({})>({})(<>)()",
"error_indices": [
4,
5,
8
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"lan... | dyck_language_reasoning_errors | null |
[
{
"content": "With numbers [5, 5, 8, 8] and operations ['+', '-', '*', '/'], get 100.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is ... | 3,066,239 | 103,066,239 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": false,
"language": "en",
"letter_words": nu... | game_of_24 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ){}>)}>)]]\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- D... | 84,973,774 | 484,973,774 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "[[(<{(<(){}>)}>)]]",
"given_count": null,
"is_solvable": null,
"language": null,
"lette... | dyck_language2 | null |
[
{
"content": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = 1 - x * y.\nand ⊗, the rules are as follows:\nwhen y is even, x ⊗ y = x + 2 - x ⊙ y;\notherwise, x ⊗ y = (1 ⊙ x) / y * 5.\nand △, the rules are as follows:\non the real number field, x △ y = y - x * y + x.\nThe preceden... | 91,007,438 | 291,007,438 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5 ⊙ 4 △ 4 ⊗ 9",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "english",
"le... | operation | null |
[
{
"content": "Given [3, 4, 4, 5], use the operations ['+', '-', '*', '/'] to obtain 36.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there i... | 71,140,433 | 171,140,433 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "en",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: })>)]\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease prov... | 123,702,610 | 523,702,610 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 5,
"full_sequence": "[(<({})>)]",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_words"... | dyck_language2 | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 19,437,618 | 819,437,618 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "{}{([][[]][]{{{}}})}{}()",
"error_indices": [
15,
18
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"... | dyck_language_reasoning_errors | null |
[
{
"content": "Fill in the blank:\n\n_____ + []⟧>}⟩})>⟩⟧>}> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
... | 146,998,021 | 546,998,021 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 12,
"full_sequence": "<{<⟦⟨<({⟨{<⟦[]⟧>}⟩})>⟩⟧>}>",
"given_count": null,
"is_solvable": null,
"language": null,... | dyck_language2 | null |
[
{
"content": "In this alphametic puzzle: NHLLN - NQLNL - QNLQ = QHNL, each letter represents a distinct digit from 0-9. Determine the digits that make the equation valid. Please end your response in the last line with the following format: The answer is $YOUR_ANSWER. $YOUR_ANSWER should be the equation with let... | 56,209,505 | 356,209,505 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": null,
"H": 4,
"I": null,
"J": null,
"K": null,
"L": 2,
"M": null,
"N": 5,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 9,539,973 | 809,539,973 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[]{}({})[{}()()](()[{[]}]())",
"error_indices": [
3,
9,
13,
17
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_so... | dyck_language_reasoning_errors | null |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"⟦⟧()⟦⟧]>)>⟧<>⟧)}[]]]⟩]⟩⟩⟩>}⟩}⟧>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the res... | 44,817,638 | 444,817,638 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 21,
"full_sequence": "<⟦{⟨{<⟨⟨⟨[⟨[[{(⟦⟦<(<[⟦⟧()⟦⟧]>)>⟧<>⟧)}[]]]⟩]⟩⟩⟩>}⟩}⟧>",
"given_count": null,
"is_solvable":... | dyck_language2 | null |
[
{
"content": "In this alphametic puzzle: CVXFF - CCV - NNFN - CVCV = FNFVF, each letter represents a distinct digit from 0-9. Determine the digits that make the equation valid. Please end your response in the last line with the following format: The answer is $YOUR_ANSWER. $YOUR_ANSWER should be the equation wi... | 24,264,710 | 324,264,710 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": 4,
"D": null,
"E": null,
"F": 2,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": 8,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "Let S = \")}>)]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "```[(<{()... | 54,590,824 | 454,590,824 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 5,
"full_sequence": "[(<{()}>)]",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_words"... | dyck_language2 | null |
[
{
"content": "Solve the following Sudoku puzzle. Fill in the empty cells (marked with '.') with digits 1-9.\n\nRules:\n- Each row must contain digits 1-9 with no repetition\n- Each column must contain digits 1-9 with no repetition\n- Each 3x3 box must contain digits 1-9 with no repetition\n\nPuzzle:\n```\n...68... | 34,560,009 | 734,560,009 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 29,
"is_solvable": null,
"language": "en",
"letter_words": n... | sudoku | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 94,994,031 | 894,994,031 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "(){}{}[[()](){{()}}]{()}()[]{}",
"error_indices": [
3,
19,
25,
29,
31
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": nul... | dyck_language_reasoning_errors | null |
[
{
"content": "分析以下逻辑表达式：\n\nA. not (not ((4 * -9 * 9 * 8) < (41 % 5)))\nB. (not not ((韩国的首都是开罗。) and ((-15 + -15) <= (1 - -16)))) or ((not not (法国大革命开始发生在1779年。)) and ((10 * 7 - -7 * 9) == (-20 + -5)))\nC. not not (((法国大革命开始发生在1791年。) or ((-18 - -1) >= (-15 + 20))) and (not not (日本位于亚洲。)))\n\n判断哪些表达式为真。在 \\boxe... | 39,923,599 | 639,923,599 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not (not ((4 * -9 * 9 * 8) < (41 % 5)))",
"True"
],
[
"(not not ((韩国的首都是开罗。) and ((-15 + -15) <= (1 - -16))))... | boolean_expressions | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⦅⦆⦄⦃⦄⟩}]⦆⦆}⟨⟩⦃⦄[]⦃⦄⦅⦆⟨⟩()⦅⦆⟦⟧)]⟨⟩⦅⦆\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to f... | 118,917,073 | 518,917,073 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 9,
"full_sequence": "[({⦅⦅[{⟨⦃⦅⦆⦄⦃⦄⟩}]⦆⦆}⟨⟩⦃⦄[]⦃⦄⦅⦆⟨⟩()⦅⦆⟦⟧)]⟨⟩⦅⦆",
"given_count": null,
"is_solvable": null,
... | dyck_language2 | null |
[
{
"content": "定义 ◎，规则如下：\n当y是偶数时，x ◎ y = y / y / x；\n其他情况下，x ◎ y = y * x。\n和 ☆，规则如下：\n当x大于y时，x ☆ y = y + x + (x)；\n其他情况下，x ☆ y = x / y ◎ 4 * x。\n运算优先级：** > * = / = % = ☆ > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ☆ 6 ◎ 10\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
}... | 61,354,163 | 261,354,163 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "2 ☆ 6 ◎ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"lette... | operation | null |
[
{
"content": "In this alphametic puzzle: YMLS + MGGGYU + YMSPQQ - SUYMSP = QSLLMGL, each letter represents a distinct digit from 0-9. Determine the digits that make the equation valid. Please end your response in the last line with the following format: The answer is $YOUR_ANSWER. $YOUR_ANSWER should be the equ... | 28,865,187 | 328,865,187 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": 4,
"H": null,
"I": null,
"J": null,
"K": null,
"L": 6,
"M": 5,
"N": null,
"O": null,
"P": 0,
"Q... | cryptarithm | null |
[
{
"content": "解决密码算术谜题：XXTTVT + JTYSVV - MSJS = SYSTSS（其中XXTTVT是6位数、JTYSVV是6位数、MSJS是4位数、SYSTSS是6位数），其中每个字母表示0-9之间的一个数字，不同字母代表不同数字。请计算出使等式成立的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "226646 + 368544 - 9535 = 5856... | 28,446,723 | 328,446,723 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": null,
"F": null,
"G": null,
"H": null,
"I": null,
"J": 3,
"K": null,
"L": null,
"M": 9,
"N": null,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "Fill in the blank:\n\n_____ + ]⟦⟧){})⟧>⟩]> = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},... | 17,226,341 | 417,226,341 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "<[⟨<⟦(([]⟦⟧){})⟧>⟩]>",
"given_count": null,
"is_solvable": null,
"language": null,
"let... | dyck_language2 | null |
[
{
"content": "数字 [1, 1, 2, 7]，想办法通过 ['+', '-', '*'] 计算出 100。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\nNone```",
"reasoning_content": null,
"ro... | 18,320,773 | 118,320,773 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": false,
"language": "zh",
"letter_words": nu... | game_of_24 | null |
[
{
"content": "Let S = \")⟩>)⟧}[]]}>]}]<>))⟩]}⟩⟩>\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"c... | 29,055,748 | 429,055,748 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "<⟨⟨{[⟨(([{[<{[{⟦(<⟨()⟩>)⟧}[]]}>]}]<>))⟩]}⟩⟩>",
"given_count": null,
"is_solvable": null,
... | dyck_language2 | null |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"{}]}}]))()){}[]]()}]))]]]}]]}]}})\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the r... | 171,718,028 | 571,718,028 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 23,
"full_sequence": "({{[{[[{[[[(([{[((([{{[{}]}}]))()){}[]]()}]))]]]}]]}]}})",
"given_count": null,
"is_solvab... | dyck_language2 | null |
[
{
"content": "Let S = \"⟧>]⟩⦄}⟧]]}⟩}⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"content": "`... | 8,077,358 | 408,077,358 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "⟨{⟨{[[⟦{⦃⟨[<⟦⟧>]⟩⦄}⟧]]}⟩}⟩",
"given_count": null,
"is_solvable": null,
"language": null,... | dyck_language2 | null |
[
{
"content": "定义 ◇，规则如下：\n实数域上，x ◇ y = x * y。\n运算优先级：** > * = / = % = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ◇ 10 ◇ 7 / 10\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "\\boxed{35}",
"reasoning_content": null,
"role": "assistant"
}
] | 61,196,431 | 261,196,431 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5 ◇ 10 ◇ 7 / 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"... | operation | null |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 71,209,296 | 871,209,296 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "<<>>[]{<>}(<>){}()(<[]>)[]",
"error_indices": [
11,
15,
16,
22
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_so... | dyck_language_reasoning_errors | null |
[
{
"content": "Solve the following Sudoku puzzle. Fill in the empty cells (marked with '.') with digits 1-9.\n\nRules:\n- Each row must contain digits 1-9 with no repetition\n- Each column must contain digits 1-9 with no repetition\n- Each 3x3 box must contain digits 1-9 with no repetition\n\nPuzzle:\n```\n..39.... | 88,455,408 | 788,455,408 | {
"closing_sequence": null,
"depth": null,
"difficulty": "medium",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 35,
"is_solvable": null,
"language": "en",
"letter_words": n... | sudoku | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 70,239,777 | 870,239,777 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[[()([({})]())]]{}",
"error_indices": [
3,
4,
18
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"... | dyck_language_reasoning_errors | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: <<⟨⟨{⟨[⟨(\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProvide only the complet... | 71,729,412 | 71,729,412 | {
"closing_sequence": ")⟩]⟩}⟩⟩>>",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 9,
"full_sequence": "<<⟨⟨{⟨[⟨()⟩]⟩}⟩⟩>>",
"given_count": null,
"is_solvable": null,
"language": null,
... | dyck_language | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ⟦{}⟦[<{{<[⦃⦄⟦(⦃(⟦⦃(<⟦<{[⟨\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProvide ... | 98,094,763 | 98,094,763 | {
"closing_sequence": "⟩]}>⟧>)⦄⟧)⦄)⟧]>}}>]⟧⟧",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 21,
"full_sequence": "⟦{}⟦[<{{<[⦃⦄⟦(⦃(⟦⦃(<⟦<{[⟨⟩]}>⟧>)⦄⟧)⦄)⟧]>}}>]⟧⟧",
"given_count": null,
"... | dyck_language | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: [[<⟨⟩(⟦{⦃⦄}⟧)>(())]][]<>{}{[]}⟦[<<{⦃⟨⟦⦃<\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is requi... | 99,561,997 | 99,561,997 | {
"closing_sequence": ">⦄⟧⟩⦄}>>]⟧",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 10,
"full_sequence": "[[<⟨⟩(⟦{⦃⦄}⟧)>(())]][]<>{}{[]}⟦[<<{⦃⟨⟦⦃<>⦄⟧⟩⦄}>>]⟧",
"given_count": null,
"is_solv... | dyck_language | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ]}]>]]>]])}]\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlea... | 116,772,396 | 516,772,396 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 12,
"full_sequence": "[{([[<[[<[{[]}]>]]>]])}]",
"given_count": null,
"is_solvable": null,
"language": null,
... | dyck_language2 | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ))>)>\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease prov... | 18,453,996 | 418,453,996 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 5,
"full_sequence": "<(<(())>)>",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_words"... | dyck_language2 | null |
[
{
"content": "Let S = \"⦃⦄>>])⟧]}⦄]⦄⟧⟩⟩]⟩⟧}⦄}>)⟧⦆\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
"... | 70,916,754 | 470,916,754 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 23,
"full_sequence": "⦅⟦(<{⦃{⟦⟨[⟨⟨⟦⦃[⦃{[⟦([<<⦃⦄>>])⟧]}⦄]⦄⟧⟩⟩]⟩⟧}⦄}>)⟧⦆",
"given_count": null,
"is_solvable": nul... | dyck_language2 | null |
[
{
"content": "解决密码算术谜题：EZENG + GZ + EEZ = EEZGN（其中EZENG是5位数、GZ是2位数、EEZ是3位数、EEZGN是5位数），其中每个字母表示0-9之间的一个数字，不同字母代表不同数字。请计算出使等式成立的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "87806 + 67 + 887 = 88760",
"reasoning_c... | 45,937,362 | 345,937,362 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": 8,
"F": null,
"G": 6,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": null,
"N": 0,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "With numbers [1, 2, 10, 10] and operations ['+', '-', '*', '/'], get 72.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is... | 98,112,539 | 198,112,539 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": false,
"language": "en",
"letter_words": nu... | game_of_24 | null |
[
{
"content": "Sudoku Challenge:\n\n```\n.9....4.3\n6287.4...\n34.9.872.\n1...46...\n..71293..\n.69.87512\n..6.7...1\n5...6.97.\n..3.9...5\n```\n\nFill in the blanks ('.') following standard Sudoku rules. Output the complete solution grid wrapped in ``` marks.",
"reasoning_content": null,
"role": "user"
... | 75,351,718 | 775,351,718 | {
"closing_sequence": null,
"depth": null,
"difficulty": "easy",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 39,
"is_solvable": null,
"language": "en",
"letter_words": nul... | sudoku | null |
[
{
"content": "Define ⊕, the rules are as follows:\nwhen y is a multiple of 3, x ⊕ y = y + x;\notherwise, x ⊕ y = x - x ** y.\nand □, the rules are as follows:\nwhen y is a multiple of 3, x □ y = y + y - x;\notherwise, x □ y = 1 * x ⊕ y.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y ... | 47,079,457 | 247,079,457 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "9 ⊕ 3 □ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "english",
"lette... | operation | null |
[
{
"content": "You are an expert in Dyck language, where you must complete bracket sequences (e.g., [], {}, <>). You need to analyze whether the bracket matching steps are correct according to Dyck language rules.\n\nGiven an initial Dyck language sequence and steps for deriving the closing bracket sequence (giv... | 84,216,063 | 884,216,063 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[[([])()]]()",
"error_indices": [
4,
6,
9
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"languag... | dyck_language_reasoning_errors | null |
[
{
"content": "数字 [5, 5, 6, 7, 7, 8]，目标 36，可用运算：['+', '-', '*', '/']。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n6*(7-(5+8/(5-7)))```",
"reasoning_co... | 76,449,253 | 176,449,253 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "zh",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "Given: RVRVR + VRPVMR = DPUUDD, where each letter represents a unique digit (RVRVR is a 5-digit number, VRPVMR is a 6-digit number, and DPUUDD is a 6-digit number). Find the numeric equation that makes the equality valid. Please end your response in the last line with the following format: The ans... | 34,505,386 | 334,505,386 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": 6,
"E": null,
"F": null,
"G": null,
"H": null,
"I": null,
"J": null,
"K": null,
"L": null,
"M": 0,
"N": null,
"O": null,
"P": 7,
... | cryptarithm | null |
[
{
"content": "研究以下逻辑语句：\n\nA. ((((13 + 0) <= (2 ** 1)) and (((4 ** 1) >= (-2 - -5)) or (油在常温下是液体。)) and (秘鲁位于南美洲。)) and (not (not ((9 + 6) >= (-9 - 9))))) and (not not ((-3 * 0 - -10 * 6) == (2 * 17))) and ((((9 - 8) >= (3 ** 3)) and ((1964年奥运会在赫尔辛基举办。) or (氧气在常温下是固体。)) and (not ((573是斐波那契数。) and ((-18 * -13) >... | 25,241,846 | 625,241,846 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((((13 + 0) <= (2 ** 1)) and (((4 ** 1) >= (-2 - -5)) or (油在常温下是液体。)) and (秘鲁位于南美洲。)) and (not (not ((9 + 6) >= (-9 - 9))))) and ... | boolean_expressions | null |
[
{
"content": "数字 [4, 10, 11, 11, 12]，想办法通过 ['+', '-', '*', '/'] 计算出 72。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n(10-11*4/11)*12```",
"reasoning_c... | 70,414,223 | 170,414,223 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "zh",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ()⟩)>)⟩))]}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- ... | 197,517,429 | 597,517,429 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 9,
"full_sequence": "{[((⟨(<(⟨()⟩)>)⟩))]}",
"given_count": null,
"is_solvable": null,
"language": null,
"let... | dyck_language2 | null |
[
{
"content": "Evaluate each expression below:\n\nA. not (Spain is in Antarctica.)\nB. ((not ((-5 + 12) > (-1 * 1 - 5 * 0))) and (A mosquito is a fish.)) or ((((6 + -3) > (4 + -15)) and (92 is less than or equal to 26.)) or (((0 - 8) != (16 * 13)) and ((5 * 17) != (4 - 7))))\nC. (((Iron is a gas at room temperat... | 11,406,674 | 611,406,674 | {
"closing_sequence": null,
"depth": 3,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"not (Spain is in Antarctica.)",
"True"
],
[
"((not ((-5 + 12) > (-1 * 1 - 5 * 0))) and (A mosquito is a fish.... | boolean_expressions | null |
[
{
"content": "利用 [3, 3, 11, 15, 16] 和 ['+', '-', '*'] 计算 60。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n15*((3*3-16)+11)```",
"reasoning_content": n... | 56,573,916 | 156,573,916 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "zh",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"<>)}})[]⟧⟧}()]><>}}{}⟧}⟧()⟨⟩]]}()<>}<>>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer ... | 49,770,018 | 449,770,018 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 19,
"full_sequence": "<{{[[⟦{⟦{{<[{⟦⟦({{(<>)}})[]⟧⟧}()]><>}}{}⟧}⟧()⟨⟩]]}()<>}<>>",
"given_count": null,
"is_solv... | dyck_language2 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ]}]()>]>}<>}()}[]<>)]<>}>))])[]}[]]{}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to... | 50,137,163 | 450,137,163 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 19,
"full_sequence": "[{([((<{[({{{<[<[{[]}]()>]>}<>}()}[]<>)]<>}>))])[]}[]]{}",
"given_count": null,
"is_solvab... | dyck_language2 | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ⟦[]⟧<⟨{}⟩{{}{<<⟦⟧⟨⟦⟧⦃⟦(⦃{<⟨\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n\nProvid... | 61,971,399 | 61,971,399 | {
"closing_sequence": "⟩>}⦄)⟧⦄⟩>>}}>",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 13,
"full_sequence": "⟦[]⟧<⟨{}⟩{{}{<<⟦⟧⟨⟦⟧⦃⟦(⦃{<⟨⟩>}⦄)⟧⦄⟩>>}}>",
"given_count": null,
"is_solvable": ... | dyck_language | null |
[
{
"content": "Complete the following Dyck language sequence by adding the minimal necessary closing brackets.\n\nSequence: ()(<⟦⟧[]⟦⟧<>[⟨<>⟩⟨{{⟦⟨⟩⟧⟦<{⟨([(⟨⟨⟦{\n\nRules:\n- Add only the closing brackets needed to match all unmatched opening brackets\n- Do not add any extra bracket pairs beyond what is required\n... | 71,142,536 | 71,142,536 | {
"closing_sequence": "}⟧⟩⟩)])⟩}>⟧}}⟩]>)",
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 17,
"full_sequence": "()(<⟦⟧[]⟦⟧<>[⟨<>⟩⟨{{⟦⟨⟩⟧⟦<{⟨([(⟨⟨⟦{}⟧⟩⟩)])⟩}>⟧}}⟩]>)",
"given_count": null,
... | dyck_language | null |
[
{
"content": "已知字母等式：IIEUSS - EISMU - UTEUU = EMUUI（其中IIEUSS是6位数、EISMU是5位数、UTEUU是5位数、EMUUI是5位数），每个字母代表一个数字，不同字母代表不同数字。请找出让等式成立的数字替换方案。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "229400 - 92014 - 45944 = 91442",
"re... | 68,757,293 | 368,757,293 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": null,
"D": null,
"E": 9,
"F": null,
"G": null,
"H": null,
"I": 2,
"J": null,
"K": null,
"L": null,
"M": 1,
"N": null,
"O": null,
"P": null,
... | cryptarithm | null |
[
{
"content": "Solve the following Sudoku puzzle. Fill in the empty cells (marked with '.') with digits 1-9.\n\nRules:\n- Each row must contain digits 1-9 with no repetition\n- Each column must contain digits 1-9 with no repetition\n- Each 3x3 box must contain digits 1-9 with no repetition\n\nPuzzle:\n```\n6.8..... | 21,032,366 | 721,032,366 | {
"closing_sequence": null,
"depth": null,
"difficulty": "easy",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 38,
"is_solvable": null,
"language": "en",
"letter_words": nul... | sudoku | null |
[
{
"content": "A sequence of brackets was cut, and only the end remains:\n\n\"]⟨⟩⟩}⟩<><>⟩⟨⟩{})>}[]<>()()⟨⟩\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restor... | 60,691,503 | 460,691,503 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "{<(⟨⟨{⟨[]⟨⟩⟩}⟩<><>⟩⟨⟩{})>}[]<>()()⟨⟩",
"given_count": null,
"is_solvable": null,
"languag... | dyck_language2 | null |
[
{
"content": "Given the following boolean expressions:\n\nA. ((A tuna is a fish.) and ((((-1 * -5 - -8 * 10) == (-16 * 8)) or (Australia is in Oceania.)) or ((The human body has 150 bones.) and (The currency of European Union is the Rand.)))) or (((9 * 6) != (10 - 20)) and (not not (Jupiter is the 4th planet fr... | 71,152,242 | 671,152,242 | {
"closing_sequence": null,
"depth": 4,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((A tuna is a fish.) and ((((-1 * -5 - -8 * 10) == (-16 * 8)) or (Australia is in Oceania.)) or ((The human body has 150 bones.) ... | boolean_expressions | null |
[
{
"content": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: )<>]]<>()()>]]}][]()\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balan... | 16,014,516 | 416,014,516 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 8,
"full_sequence": "[{[[<[[()<>]]<>()()>]]}][]()",
"given_count": null,
"is_solvable": null,
"language": null... | dyck_language2 | null |
[
{
"content": "研究以下逻辑语句：\n\nA. (13 + 14) >= (-10 * -3 - 6 * 3)\nB. ((-10 * 15) >= (-3 * -15)) and (酒精在常温下是气体。)\nC. (not (鸡有6条腿。)) and ((蝙蝠是哺乳动物。) or (金星是距离太阳第6近的行星。))\nD. (not (丹麦的货币是克朗。)) or (not not (匈牙利的首都是布达佩斯。))\nE. (((-5 * -3 * -9 * -4) <= (-18 * 15)) or ((14 + 1) <= (-1 * -9 + -3 * 3))) and ((泰坦尼克号沉没发生在19... | 13,366,497 | 613,366,497 | {
"closing_sequence": null,
"depth": 2,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"(13 + 14) >= (-10 * -3 - 6 * 3)",
"True"
],
[
"((-10 * 15) >= (-3 * -15)) and (酒精在常温下是气体。)",
"False"
... | boolean_expressions | null |
[
{
"content": "Let S = \"()⟩⟩⟦⟧⟧⟧]⦆⟧}⦆})⟨⟩⦅⦆>>[]⟧⦄}⟧]⟧⟧\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},
{
... | 100,172,418 | 500,172,418 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 20,
"full_sequence": "⟦⟦[⟦{⦃⟦<<({⦅{⟦⦅[⟦⟦⟨⟨()⟩⟩⟦⟧⟧⟧]⦆⟧}⦆})⟨⟩⦅⦆>>[]⟧⦄}⟧]⟧⟧",
"given_count": null,
"is_solvable": n... | dyck_language2 | null |
[
{
"content": "完成这道数独题目。将每个'.'替换为1到9之间的数字。\n\n```\n.6483.275\n3...42.6.\n.......43\n......5..\n.3....1..\n6.532....\n...2..4..\n.........\n.216.....\n```\n\n规则：每行、每列、每个3x3宫格都必须恰好包含数字1-9各一次。\n\n以相同格式输出解答，用三个反引号包裹。",
"reasoning_content": null,
"role": "user"
},
{
"content": "164839275\n359742861\n8... | 10,480,652 | 710,480,652 | {
"closing_sequence": null,
"depth": null,
"difficulty": "hard",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 25,
"is_solvable": null,
"language": "zh",
"letter_words": nul... | sudoku | null |
[
{
"content": "定义 △，规则如下：\n当y是奇数时，x △ y = y - x + x；\n其他情况下，x △ y = (y - x - y)。\n运算优先级：** > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 * 2 / 4 △ 3\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
{
"content": "\\boxed{-0.5}",
"reasoning_content": null,
... | 35,595,842 | 235,595,842 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "1 * 2 / 4 △ 3",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"le... | operation | null |
[
{
"content": "Numbers [3, 4, 5, 8, 8], find a way to get 36 using ['+', '-', '*'].\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no ... | 57,625,798 | 157,625,798 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "en",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "给定以下布尔表达式：\n\nA. ((((not (猫有8条腿。)) and ((丹麦的首都是河内。) and (埃及位于大洋洲。))) and (not not ((0 + -7) != (8 * 5 * -5 * 9)))) or ((not not (现代奥运会首届举办发生在1896年。)) or ((铬的化学符号是Cr。) and (伦敦大火发生在1668年。)) or ((希腊的首都是布加勒斯特。) or ((1919年是闰年。) or ((42 % 10) > (-16 + 8)))))) and ((not (((新西兰位于亚洲。) or (第一次世界大战开始发生在1914年... | 9,501,289 | 609,501,289 | {
"closing_sequence": null,
"depth": 5,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": [
[
"((((not (猫有8条腿。)) and ((丹麦的首都是河内。) and (埃及位于大洋洲。))) and (not not ((0 + -7) != (8 * 5 * -5 * 9)))) or ((not not (现代奥运会首届举办发生在1896年... | boolean_expressions | null |
[
{
"content": "定义 ♢，规则如下：\n当y是3的倍数时，x ♢ y = x + y * 2 + y ** 2；\n其他情况下，x ♢ y = y - y / x * y + y。\n和 ◇，规则如下：\n当y是奇数时，x ◇ y = y - y * y + x + x；\n其他情况下，x ◇ y = (y ♢ x) * x ** x - y。\n和 ☆，规则如下：\n当y是偶数时，x ☆ y = y * y + y * x / x；\n其他情况下，x ☆ y = 4 - 2 + x - y * x。\n运算优先级：♢ > ◇ > ** > * = / = % > + = - = ... | 8,022,922 | 208,022,922 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5 ☆ 4 + 3 / 10 ♢ 3 ◇ 10",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chine... | operation | null |
[
{
"content": "给定一个字母等式：WFWCO * CEGE = WEEYLCYLC，每个字母表示一个数字，不同字母表示不同数字。其中WFWCO是5位数，CEGE是4位数，WEEYLCYLC是9位数。请计算出满足条件的数字等式。 请在回答的最后一行使用以下格式：答案是 $YOUR_ANSWER。$YOUR_ANSWER 应该是替换为数字后的等式。",
"reasoning_content": null,
"role": "user"
},
{
"content": "19183 * 8656 = 166048048",
"reasoning_content": nul... | 1,237,939 | 301,237,939 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": {
"A": null,
"B": null,
"C": 8,
"D": null,
"E": 6,
"F": 9,
"G": 5,
"H": null,
"I": null,
"J": null,
"K": null,
"L": 4,
"M": null,
"N": null,
"O": 3,
"P": null,
"Q": nul... | cryptarithm | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: )⟦⟧>⟧[]⟨⟩)>[]>{}>()>]()})⟧⟧>⟧>\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets... | 155,881,294 | 555,881,294 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 16,
"full_sequence": "<⟦<⟦⟦({[<<<<(⟦<()⟦⟧>⟧[]⟨⟩)>[]>{}>()>]()})⟧⟧>⟧>",
"given_count": null,
"is_solvable": null,... | dyck_language2 | null |
[
{
"content": "定义 ☆，规则如下：\n当x和y的和是偶数时，x ☆ y = 1 / 1 / x / y / 2；\n其他情况下，x ☆ y = y + x + y * x。\n和 ♡，规则如下：\n当y是3的倍数时，x ♡ y = y * y - y - x / x；\n其他情况下，x ♡ y = y + x + x。\n运算优先级：☆ > ** > * = / = % = ♡ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ☆ 4 ♡ 9\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,... | 85,354,738 | 285,354,738 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "5 ☆ 4 ♡ 9",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"letter... | operation | null |
[
{
"content": "Fill in the blank:\n\n_____ + <>]⟨⟩<>}{}[] = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`.",
"reasoning_content": null,
"role": "user"
},... | 110,044,709 | 510,044,709 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 2,
"full_sequence": "{[<>]⟨⟩<>}{}[]",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_wo... | dyck_language2 | null |
[
{
"content": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = x + 1 * abs(x) / y。\n和 ☆，规则如下：\n实数域上，x ☆ y = x + y * y * x * y。\n和 □，规则如下：\n实数域上，x □ y = y - x ⊙ x。\n运算优先级：⊙ > □ > ** > * = / = % > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ⊙ 1 ☆ 7\n请将最终答案填入\\boxed{}中。",
"reasoning_content": null,
"role": "user"
},
... | 87,508,392 | 287,508,392 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": "1 ⊙ 1 ☆ 7",
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": "chinese",
"letter... | operation | null |
[
{
"content": "用 [1, 1, 2, 4, 4, 8] 这几个数字，运算 ['+', '-', '*', '/']，目标 60。\n\n在回答的最后，请输出一个 ```python 代码块。代码块中仅包含一个代表答案的表达式，并且该表达式可以直接被 Python 中的 eval() 函数求值。如果无解，请输出 ```python\\nNone\\n```。",
"reasoning_content": null,
"role": "user"
},
{
"content": "```python\n4*((8+(1+4))+2)/1```",
"reasoning... | 56,429,674 | 156,429,674 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": true,
"language": "zh",
"letter_words": nul... | game_of_24 | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ()()[])]][]()\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPle... | 142,138,058 | 542,138,058 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 3,
"full_sequence": "[[(()()[])]][]()",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_... | dyck_language2 | null |
[
{
"content": "Given [8, 12, 14, 15], use arithmetic ['+', '-', '*', '/'] to get 60.\n\nAt the end of your response, please output a ```python code block. The code block should contain only a single expression representing the answer, which can be directly evaluated using Python's eval() function. If there is no... | 51,548,396 | 151,548,396 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": false,
"language": "en",
"letter_words": nu... | game_of_24 | null |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 10,639,114 | 810,639,114 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "(){}(())[]",
"error_indices": [
7,
11
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"language": null... | dyck_language_reasoning_errors | null |
[
{
"content": "Solve the following Sudoku puzzle. Fill in the empty cells (marked with '.') with digits 1-9.\n\nRules:\n- Each row must contain digits 1-9 with no repetition\n- Each column must contain digits 1-9 with no repetition\n- Each 3x3 box must contain digits 1-9 with no repetition\n\nPuzzle:\n```\n56..8... | 84,465,454 | 784,465,454 | {
"closing_sequence": null,
"depth": null,
"difficulty": "easy",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 37,
"is_solvable": null,
"language": "en",
"letter_words": nul... | sudoku | null |
[
{
"content": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ())>)⟩]}\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease p... | 95,303,252 | 495,303,252 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": 6,
"full_sequence": "{[⟨(<(())>)⟩]}",
"given_count": null,
"is_solvable": null,
"language": null,
"letter_wo... | dyck_language2 | null |
[
{
"content": "Sudoku Challenge:\n\n```\n.......17\n....81..4\n28.74...3\n.......8.\n.6..2.3..\n........2\n......2..\n..98.2...\n...96.1..\n```\n\nFill in the blanks ('.') following standard Sudoku rules. Output the complete solution grid wrapped in ``` marks.",
"reasoning_content": null,
"role": "user"
... | 40,762,165 | 740,762,165 | {
"closing_sequence": null,
"depth": null,
"difficulty": "hard",
"digit_map": null,
"dyck_sequence": null,
"error_indices": null,
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": 22,
"is_solvable": null,
"language": "en",
"letter_words": nul... | sudoku | null |
[
{
"content": "As a Dyck language expert, you need to verify the correctness of bracket matching reasoning steps.\n\nA Dyck sequence must have all brackets properly matched and nested. The reasoning process tracks a stack: opening brackets are pushed, and closing brackets pop the matching opening bracket.\n\nSeq... | 46,359,541 | 846,359,541 | {
"closing_sequence": null,
"depth": null,
"difficulty": null,
"digit_map": null,
"dyck_sequence": "[[()]]([])[[]()]",
"error_indices": [
7,
10,
13
],
"expression": null,
"expressions": null,
"fill_length": null,
"full_sequence": null,
"given_count": null,
"is_solvable": null,
"l... | dyck_language_reasoning_errors | null |
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