env stringclasses 1
value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: <><>()⟩[]}()⟩)()>]{}⟩>⟩>(){}}>]]}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{[[<{<⟨<⟨[<(⟨{⟨<><>()⟩[]}()⟩)()>]{}⟩>⟩>(){}}>]]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "{[[<{<⟨<⟨[<(⟨{⟨<><>()⟩[]}()⟩)()>]{}⟩>⟩>(){}}>]]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{... |
logic-v2 | Let S = "))){}[]]{}}[]})]}]]]])" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "([[[[{[({{[((())){}[]]{}}[]})]}]]]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "([[[[{[({{[((())){}[]]{}}[]})]}]]]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[[{[({{[(((",
"p... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"[]⟦⟧⟩}[]]>)⟧})]⟨⟩)⟩⟧)⟧)⟩}>>⟧⟧}>>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in back... | {
"game_data": {
"answer": "<<{⟦⟦<<{⟨(⟦(⟦⟨([({⟦(<[{⟨[]⟦⟧⟩}[]]>)⟧})]⟨⟩)⟩⟧)⟧)⟩}>>⟧⟧}>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 24,
"full_sequence": "<<{⟦⟦<<{⟨(⟦(⟦⟨([({⟦(<[{⟨[]⟦⟧⟩}[]]>)⟧})]⟨⟩)⟩⟧)⟧)⟩}>>⟧⟧}>>",
"n_types": 6,
"nesting_depth": 0,
"ope... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦃⦄]]⦄}⦄>)⦄)⟧}⟧>)⦄⟧⟧⟩⟩
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extr... | {
"game_data": {
"answer": "⟨⟨⟦⟦⦃(<⟦{⟦(⦃(<⦃{⦃[[⦃⦄]]⦄}⦄>)⦄)⟧}⟧>)⦄⟧⟧⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "⟨⟨⟦⟦⦃(<⟦{⟦(⦃(<⦃{⦃[[⦃⦄]]⦄}⦄>)⦄)⟧}⟧>)⦄⟧⟧⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⟦⟦⦃(<⟦{⟦(⦃(<⦃{⦃... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: >[]⟦⟧⟦⟧]⟧<>⟩⟩⟦⟧]]>⟨⟩>⟨⟩
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks l... | {
"game_data": {
"answer": "<<[[⟨⟨⟦[<>[]⟦⟧⟦⟧]⟧<>⟩⟩⟦⟧]]>⟨⟩>⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "<<[[⟨⟨⟦[<>[]⟦⟧⟦⟧]⟧<>⟩⟩⟦⟧]]>⟨⟩>⟨⟩",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<[[⟨⟨⟦[<",
"prompt_name": "... |
logic-v2 | Q: What opening brackets should precede "⟨⟩)()[]>⟦⟧<>)⟧}⟩⦃⦄<>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨{⟦(<(⟨⟩)()[]>⟦⟧<>)⟧}⟩⦃⦄<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⟨{⟦(<(⟨⟩)()[]>⟦⟧<>)⟧}⟩⦃⦄<>",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⟦(<(",
"prompt_name": "qa",
"pro... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: {}}[]}{}}])]]}))}})]})}})
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your fi... | {
"game_data": {
"answer": "({{({[({{(({[[([{{{{}}[]}{}}])]]}))}})]})}})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "({{({[({{(({[[([{{{{}}[]}{}}])]]}))}})]})}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{({[({{... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟦⟧]⟧)⦆[]⟨⟩[])⦄>⦆[]⟩⟧⦄"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like ... | {
"game_data": {
"answer": "⦃⟦⟨⦅<⦃(⦅(⟦[⟦⟧]⟧)⦆[]⟨⟩[])⦄>⦆[]⟩⟧⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⦃⟦⟨⦅<⦃(⦅(⟦[⟦⟧]⟧)⦆[]⟨⟩[])⦄>⦆[]⟩⟧⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⟦⟨⦅<⦃(⦅(⟦[",
"prompt_name"... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ]{}()[])}[])])()
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bra... | {
"game_data": {
"answer": "([({([]{}()[])}[])])()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "([({([]{}()[])}[])])()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([({([",
"prompt_name": "direct",
"prompt_... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: >]{}())])>>]]}]])>}]]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks lik... | {
"game_data": {
"answer": "[[{<([[{[[<<([([<>]{}())])>>]]}]])>}]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "[[{<([[{[[<<([([<>]{}())])>>]]}]])>}]]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{<([[{[[<<([([<",
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟩)>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the comple... | {
"game_data": {
"answer": "<(⟨⟩)>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "<(⟨⟩)>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(⟨",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"se... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟨⟩{}()]}⟨⟩[]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{[⟨⟩{}()]}⟨⟩[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "{[⟨⟩{}()]}⟨⟩[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[",
"prompt_name": "technical",
"prompt_variant": 3,
... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: [])}]{}}{}])}){}])}))}}}()){}()()()
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "({{{(({([({([{[{([])}]{}}{}])}){}])}))}}}()){}()()()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "({{{(({([({([{[{([])}]{}}{}])}){}])}))}}}()){}()()()",
"n_types": 3,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"]{}[]][](){})])}]}]])"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like ... | {
"game_data": {
"answer": "([[{[{([([[]{}[]][](){})])}]}]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "([[{[{([([[]{}[]][](){})])}]}]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[{[{([([[",
"prompt_name"... |
logic-v2 | Q: What opening brackets should precede "[][]{}]]{}}]}][])))))]]]]])}}]])" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([[{{([[[[[((((([{[{[[[][]{}]]{}}]}][])))))]]]]])}}]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"full_sequence": "([[{{([[[[[((((([{[{[[[][]{}]]{}}]}][])))))]]]]])}}]])",
"n_types": 3,
"nesting_depth": 0,
"opening... |
logic-v2 | Let S = "><>}}][]]{}" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[[{{<><>}}][]]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[[{{<><>}}][]]{}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{{<",
"prompt_name": "mathematical",
"prompt_variant... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: {})(){}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "({})(){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "({})(){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 142... |
logic-v2 | Fill in the blank:
_____ + ⦄⦃⦄)⟩⦄⦄)⦃⦄[]⟦⟧⦄{}})>>>⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨<<<({⦃(⦃⦃⟨(⦃⦄⦃⦄)⟩⦄⦄)⦃⦄[]⟦⟧⦄{}})>>>⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⟨<<<({⦃(⦃⦃⟨(⦃⦄⦃⦄)⟩⦄⦄)⦃⦄[]⟦⟧⦄{}})>>>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<<<({⦃(⦃⦃⟨(⦃",
"pr... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟨⟩)]⟧}⟩⟩()}))⟩<>⟨⟩>>⟩⟧]⟧⟩]}⟧>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backt... | {
"game_data": {
"answer": "<⟦{[⟨⟦[⟦⟨<<⟨(({⟨⟨{⟦[(⟨⟩)]⟧}⟩⟩()}))⟩<>⟨⟩>>⟩⟧]⟧⟩]}⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "<⟦{[⟨⟦[⟦⟨<<⟨(({⟨⟨{⟦[(⟨⟩)]⟧}⟩⟩()}))⟩<>⟨⟩>>⟩⟧]⟧⟩]}⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Let S = "}⦄()⟩⟩⟩]⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[⟨⟨⟨⦃{}⦄()⟩⟩⟩]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⟨[⟨⟨⟨⦃{}⦄()⟩⟩⟩]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟨⟨⟨⦃{",
"prompt_name": "mathematical",
"prompt_varia... |
logic-v2 | Let S = "}])[][]}<>]}])])})))})]}])]}]}>]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[<{[{[([{[({((({([([{[{([{}])[][]}<>]}])])})))})]}])]}]}>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 26,
"full_sequence": "[<{[{[([{[({((({([([{[{([{}])[][]}<>]}])])})))})]}])]}]}>]",
"n_types": 4,
"nesting_depth": 0,
... |
logic-v2 | Q: What opening brackets should precede "}}])[]}>>]>]()()<>(){}{}()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<[<<{([{{}}])[]}>>]>]()()<>(){}{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "[<[<<{([{{}}])[]}>>]>]()()<>(){}{}()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<[<<{([{{",
"promp... |
logic-v2 | Let S = "}<>]{}}]>{}}[]()]()>]{}<>[]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[<[{<[{[{}<>]{}}]>{}}[]()]()>]{}<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[<[{<[{[{}<>]{}}]>{}}[]()]()>]{}<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<[{<[{[{",
"prompt_... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ()⟨⟩}])⟨⟩⟩}()}⟩]}>>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like ... | {
"game_data": {
"answer": "<<{[⟨{{⟨([{()⟨⟩}])⟨⟩⟩}()}⟩]}>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "<<{[⟨{{⟨([{()⟨⟩}])⟨⟩⟩}()}⟩]}>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<{[⟨{{⟨([{",
"prompt_name": "p... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟧⟨⟩⟧())⟧{}})⦄>⦄}⟩
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answ... | {
"game_data": {
"answer": "⟨{⦃<⦃({⟦(⟦⟦⟧⟨⟩⟧())⟧{}})⦄>⦄}⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨{⦃<⦃({⟦(⟦⟦⟧⟨⟩⟧())⟧{}})⦄>⦄}⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⦃<⦃({⟦(⟦⟦",
"prompt_name": "rever... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟨⟩⟧)"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(⟦⟨⟩⟧)",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "(⟦⟨⟩⟧)",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟦",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 105926705,... |
logic-v2 | Let S = ")⟨⟩⟩])⟩)]}()<><>)}[]<>{}[]⟨⟩()<><>[]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "{({[(⟨([⟨()⟨⟩⟩])⟩)]}()<><>)}[]<>{}[]⟨⟩()<><>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "{({[(⟨([⟨()⟨⟩⟩])⟩)]}()<><>)}[]<>{}[]⟨⟩()<><>[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{({[(... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]](){}]{})})})[]{}(){}{}{}()(){}{}{}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "({({([[[]](){}]{})})})[]{}(){}{}{}()(){}{}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "({({([[[]](){}]{})})})[]{}(){}{}{}()(){}{}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({({([[[",... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟧())]{}()}⦃⦄⟩⦄}⟩
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `an... | {
"game_data": {
"answer": "⟨{⦃⟨{[(⟦⟧())]{}()}⦃⦄⟩⦄}⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⟨{⦃⟨{[(⟦⟧())]{}()}⦃⦄⟩⦄}⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⦃⟨{[(⟦",
"prompt_name": "puzzle",
"p... |
logic-v2 | Fill in the blank:
_____ + ][]}()}{}}}}[]()){}]}))[]()[](){}{}()[]()[] = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({[({{{{{[][]}()}{}}}}[]()){}]}))[]()[](){}{}()[]()[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "(({[({{{{{[][]}()}{}}}}[]()){}]}))[]()[](){}{}()[]()[]",
"n_types": 3,
"nesting_depth": 0,
"opening... |
logic-v2 | Let S = "}}<>{})⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨({{}}<>{})⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "⟨({{}}<>{})⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨({{",
"prompt_name": "mathematical",
"prompt_variant": 5,
... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: >)}]}[]>]]}}])]<>[]<>[]{}[](){}(){}{}[]()
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequen... | {
"game_data": {
"answer": "[([{{[[<{[{(<>)}]}[]>]]}}])]<>[]<>[]{}[](){}(){}{}[]()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "[([{{[[<{[{(<>)}]}[]>]]}}])]<>[]<>[]{}[](){}(){}{}[]()",
"n_types": 4,
"nesting_depth": 0,
"opening... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]())⟨⟩>⟩⟩{}⟩⟩]<>⟩}⟦⟧()>>
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "<<{⟨[⟨⟨⟨⟨<([]())⟨⟩>⟩⟩{}⟩⟩]<>⟩}⟦⟧()>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<<{⟨[⟨⟨⟨⟨<([]())⟨⟩>⟩⟩{}⟩⟩]<>⟩}⟦⟧()>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<{⟨[⟨⟨⟨⟨<([",
"pro... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: }}])}]]}]})]]}}]}}}}})]))}})
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your... | {
"game_data": {
"answer": "({{(([({{{{{[{{[[({[{[[{([{{}}])}]]}]})]]}}]}}}}})]))}})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 28,
"full_sequence": "({{(([({{{{{[{{[[({[{[[{([{{}}])}]]}]})]]}}]}}}}})]))}})",
"n_types": 3,
"nesting_depth": 0,
"ope... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}]]()]}()))"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({[[[{}]]()]}()))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "(({[[[{}]]()]}()))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({[[[{",
"prompt_name": "story",
"prompt_variant"... |
logic-v2 | Let S = "⟩[]}>{})<>>}()}⟩>⟨⟩)⟨⟩()}())}⟨⟩{}[][][]{}()[]{}" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "{({(<⟨{{<(<{⟨⟩[]}>{})<>>}()}⟩>⟨⟩)⟨⟩()}())}⟨⟩{}[][][]{}()[]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "{({(<⟨{{<(<{⟨⟩[]}>{})<>>}()}⟩>⟨⟩)⟨⟩()}())}⟨⟩{}[][][]{}()[]{}",
"n_types": 5,
"nesting_depth": 0,
... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]⟩<><>())⦅⦆⟨⟩})⦄>⟧⟩}}⟧])⟩>⦆⦆)>⟩)⟩>⦄
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⦃<⟨(⟨<(⦅⦅<⟨([⟦{{⟨⟦<⦃({(⟨[]⟩<><>())⦅⦆⟨⟩})⦄>⟧⟩}}⟧])⟩>⦆⦆)>⟩)⟩>⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 25,
"full_sequence": "⦃<⟨(⟨<(⦅⦅<⟨([⟦{{⟨⟦<⦃({(⟨[]⟩<><>())⦅⦆⟨⟩})⦄>⟧⟩}}⟧])⟩>⦆⦆)>⟩)⟩>⦄",
"n_types": 8,
"nesting_depth": 0,
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟩⟩[]<>⟧))>⟧>⦄⦄⟧]⟧>⦄>)>⦄⟧⟧⟩⦄
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your ... | {
"game_data": {
"answer": "⦃⟨⟦⟦⦃<(<⦃<⟦[⟦⦃⦃<⟦<((⟦⟨⟨⟩⟩[]<>⟧))>⟧>⦄⦄⟧]⟧>⦄>)>⦄⟧⟧⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "⦃⟨⟦⟦⦃<(<⦃<⟦[⟦⦃⦃<⟦<((⟦⟨⟨⟩⟩[]<>⟧))>⟧>⦄⦄⟧]⟧>⦄>)>⦄⟧⟧⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }}⟨⟩⟩{}}()}]]⟩)>>}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra b... | {
"game_data": {
"answer": "{<<(⟨[[{{⟨{{}}⟨⟩⟩{}}()}]]⟩)>>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "{<<(⟨[[{{⟨{{}}⟨⟩⟩{}}()}]]⟩)>>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<<(⟨[[{{⟨{{",
"prompt_name": "... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟩⦄}]])>⟧⟩}⟩
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (th... | {
"game_data": {
"answer": "⟨{⟨⟦<([[{⦃⟨⟩⦄}]])>⟧⟩}⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨{⟨⟦<([[{⦃⟨⟩⦄}]])>⟧⟩}⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⟨⟦<([[{⦃⟨",
"prompt_name": "reverse_perspecti... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: })⟩]⟦⟧)>{}]]]{}]⟨⟩⦃⦄>[]⟩⟩
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨<[[[[<([⟨({})⟩]⟦⟧)>{}]]]{}]⟨⟩⦃⦄>[]⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⟨⟨<[[[[<([⟨({})⟩]⟦⟧)>{}]]]{}]⟨⟩⦃⦄>[]⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨<[[[[<([⟨({",
... |
logic-v2 | Fill in the blank:
_____ + ⟧>]<>[]()>[]{})>{}>()⟨⟩[]{} = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<<(<[<⟦⟧>]<>[]()>[]{})>{}>()⟨⟩[]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "<<(<[<⟦⟧>]<>[]()>[]{})>{}>()⟨⟩[]{}",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<(<[<⟦",
"prompt_name":... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: }⟨⟩()⟦⟧⦆}⟨⟩{})}]()<>⟩>]⟦⟧⟦⟧⦅⦆⟦⟧
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[<⟨[{({⦅{}⟨⟩()⟦⟧⦆}⟨⟩{})}]()<>⟩>]⟦⟧⟦⟧⦅⦆⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[<⟨[{({⦅{}⟨⟩()⟦⟧⦆}⟨⟩{})}]()<>⟩>]⟦⟧⟦⟧⦅⦆⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[<⟨[{({⦅{",
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: <>]⦆⟩⦆>]>⦆)]>))>]]⟧⦄}])⦆>]⦆
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your ... | {
"game_data": {
"answer": "⦅[<⦅([{⦃⟦[[<((<[(⦅<[<⦅⟨⦅[<>]⦆⟩⦆>]>⦆)]>))>]]⟧⦄}])⦆>]⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 25,
"full_sequence": "⦅[<⦅([{⦃⟦[[<((<[(⦅<[<⦅⟨⦅[<>]⦆⟩⦆>]>⦆)]>))>]]⟧⦄}])⦆>]⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | Fill in the blank:
_____ + {}]}}⟧⟨⟩<>>]⦄⟩()}⦄]⟩>>⦄⟧⟩⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨⟦⦃<<⟨[⦃{⟨⦃[<⟦{{[{}]}}⟧⟨⟩<>>]⦄⟩()}⦄]⟩>>⦄⟧⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "⟨⟨⟦⦃<<⟨[⦃{⟨⦃[<⟦{{[{}]}}⟧⟨⟩<>>]⦄⟩()}⦄]⟩>>⦄⟧⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⟦⦃<<⟨[⦃... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"]]{}]}))"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({[[[]]{}]}))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "(({[[[]]{}]}))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({[[[",
"prompt_name": "story",
"prompt_variant": 4,
... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⟦⟧)⟧}()}⟧]]}⟧)⟧)}>>}}})>⟧⟧>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add an... | {
"game_data": {
"answer": "<⟦⟦<({{{<<{(⟦(⟦{[[⟦{{⟦(⟦⟧)⟧}()}⟧]]}⟧)⟧)}>>}}})>⟧⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "<⟦⟦<({{{<<{(⟦(⟦{[[⟦{{⟦(⟦⟧)⟧}()}⟧]]}⟧)⟧)}>>}}})>⟧⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: []⟩]]()>]⟩
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨[<[[⟨[]⟩]]()>]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⟨[<[[⟨[]⟩]]()>]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[<[[⟨",
"prompt_name": "technical",
"prompt_variant":... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ()<>)⟨⟩)>⟩[]⦄⦄{}⟨⟩[]⦃⦄{}
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your fin... | {
"game_data": {
"answer": "⦃⦃⟨<((()<>)⟨⟩)>⟩[]⦄⦄{}⟨⟩[]⦃⦄{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⦃⦃⟨<((()<>)⟨⟩)>⟩[]⦄⦄{}⟨⟩[]⦃⦄{}",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟨<((",
"prompt_name": "reverse... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟦⟧⟧[]⟨⟩⟩)}⟩<><>⟦⟧{}<>⟦⟧
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨{(⟨⟦⟦⟧⟧[]⟨⟩⟩)}⟩<><>⟦⟧{}<>⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨{(⟨⟦⟦⟧⟧[]⟨⟩⟩)}⟩<><>⟦⟧{}<>⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{(⟨⟦",
"prompt_name": "technical",
... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: []⦅⦆)⦃⦄
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the co... | {
"game_data": {
"answer": "([]⦅⦆)⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "([]⦅⦆)⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⦄⦄⟨⟩>⦄{}⦃⦄⟦⟧⟦⟧⟦⟧})⟨⟩>][]})<>()⦃⦄<>⟧{}⟨⟩⟩"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence)... | {
"game_data": {
"answer": "⟨⟦({[<({⦃<⦃⦃⦄⦄⟨⟩>⦄{}⦃⦄⟦⟧⟦⟧⟦⟧})⟨⟩>][]})<>()⦃⦄<>⟧{}⟨⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⟨⟦({[<({⦃<⦃⦃⦄⦄⟨⟩>⦄{}⦃⦄⟦⟧⟦⟧⟦⟧})⟨⟩>][]})<>()⦃⦄<>⟧{}⟨⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_pre... |
logic-v2 | Q: What opening brackets should precede "{}()>}[]))]>]><>[]]<><>()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<[<[(({<{}()>}[]))]>]><>[]]<><>()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[<[<[(({<{}()>}[]))]>]><>[]]<><>()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<[<[(({<",
"prompt_name... |
logic-v2 | Q: What opening brackets should precede "}}]]}}))" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({{[[{{}}]]}}))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "(({{[[{{}}]]}}))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({{[[{{",
"prompt_name": "qa",
"prompt_variant": 6,
... |
logic-v2 | Let S = "{}[]]]}>]}" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "{[<{[[{}[]]]}>]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{[<{[[{}[]]]}>]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[<{[[",
"prompt_name": "mathematical",
"prompt_varian... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]{}[]⟨⟩⟩⟨⟩⟩⟩⟨⟩{})⟩[]}[]<>[]{}()
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{⟨(⟨⟨⟨[]{}[]⟨⟩⟩⟨⟩⟩⟩⟨⟩{})⟩[]}[]<>[]{}()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "{⟨(⟨⟨⟨[]{}[]⟨⟩⟩⟨⟩⟩⟩⟨⟩{})⟩[]}[]<>[]{}()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨(⟨⟨⟨[",
"promp... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⦃⦄⦅⦆⦆))}⦄}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⦃{((⦅⦃⦄⦅⦆⦆))}⦄}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{⦃{((⦅⦃⦄⦅⦆⦆))}⦄}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{⦃{((⦅",
"prompt_name": "puzzle",
"prompt_variant": 2,... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: }>}}⟩⟩]]⟨⟩>]()}>⟩}>)}⟩⟩}]>}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{<[{⟨⟨{(<{⟨<{[<[[⟨⟨{{<{}>}}⟩⟩]]⟨⟩>]()}>⟩}>)}⟩⟩}]>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "{<[{⟨⟨{(<{⟨<{[<[[⟨⟨{{<{}>}}⟩⟩]]⟨⟩>]()}>⟩}>)}⟩⟩}]>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Q: What opening brackets should precede "{}()[]}⟨⟩><>⦃⦄⟨⟩⟩}>()⦄⟨⟩)⟨⟩⟩⦄<>⟧⟩()()" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦⦃⟨(⦃<{⟨<{{}()[]}⟨⟩><>⦃⦄⟨⟩⟩}>()⦄⟨⟩)⟨⟩⟩⦄<>⟧⟩()()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⟦⦃⟨(⦃<{⟨<{{}()[]}⟨⟩><>⦃⦄⟨⟩⟩}>()⦄⟨⟩)⟨⟩⟩⦄<>⟧⟩()()",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: <>{}⟦⟧⟧⟦⟧⦃⦄()⟩)⦄⦄]⦄)()⟧⟨⟩⟩⟨⟩⟦⟧⟦⟧[]⟨⟩[]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦(⦃[⦃⦃(⟨⟦<>{}⟦⟧⟧⟦⟧⦃⦄()⟩)⦄⦄]⦄)()⟧⟨⟩⟩⟨⟩⟦⟧⟦⟧[]⟨⟩[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "⟨⟦(⦃[⦃⦃(⟨⟦<>{}⟦⟧⟧⟦⟧⦃⦄()⟩)⦄⦄]⦄)()⟧⟨⟩⟩⟨⟩⟦⟧⟦⟧[]⟨⟩[]",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨... |
logic-v2 | Q: What opening brackets should precede ">)]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[(<>)]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "[(<>)]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 184850201,
... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: <>})}{})]{}}<>}]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[{{[({({<>})}{})]{}}<>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "[{{[({({<>})}{})]{}}<>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{[({({",
"prompt_name": "technical",
... |
logic-v2 | Let S = "{}}][](){}]{})){}[][]][])])" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "([([(([[{{}}][](){}]{})){}[][]][])])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "([([(([[{{}}][](){}]{})){}[][]][])])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([([(([[{",
"prompt_... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"[]]⟩⟩}}⟦⟧[]⦄⦃⦄⦄⟩)⟧}>>⟩"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like... | {
"game_data": {
"answer": "⟨<<{⟦(⟨⦃⦃{{⟨⟨[[]]⟩⟩}}⟦⟧[]⦄⦃⦄⦄⟩)⟧}>>⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "⟨<<{⟦(⟨⦃⦃{{⟨⟨[[]]⟩⟩}}⟦⟧[]⦄⦃⦄⦄⟩)⟧}>>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<<{⟦(⟨⦃⦃{{⟨⟨[",
"p... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"<>[]}}}]]}]>}<><>()[]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like ... | {
"game_data": {
"answer": "{<[{[[{{{<>[]}}}]]}]>}<><>()[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "{<[{[[{{{<>[]}}}]]}]>}<><>()[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<[{[[{{{",
"prompt_name": "stor... |
logic-v2 | Q: What opening brackets should precede ")>}>[]){}<>>)<>](){}{}(){}{}[][]()[]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[(<(<{<()>}>[]){}<>>)<>](){}{}(){}{}[][]()[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "[(<(<{<()>}>[]){}<>>)<>](){}{}(){}{}[][]()[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<(<{<(",... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}[]]⟨⟩]}⟨⟩[]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{[[{}[]]⟨⟩]}⟨⟩[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{[[{}[]]⟨⟩]}⟨⟩[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[[{",
"prompt_name": "story",
"prompt_variant": 4,
... |
logic-v2 | Q: What opening brackets should precede "[][]})){}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({[][]})){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "(({[][]})){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": ... |
logic-v2 | Fill in the blank:
_____ + )]()]}}[])}{})]}]}[])[][] = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({[{[({({{[[()]()]}}[])}{})]}]}[])[][]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "({[{[({({{[[()]()]}}[])}{})]}]}[])[][]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[{[({({{[[(",
... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ])}}{}<>()()⟨⟩{}[]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{{([])}}{}<>()()⟨⟩{}[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{{([])}}{}<>()()⟨⟩{}[]",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{([",
"prompt_name": "technical",
"prompt... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: }{}}()[])][])}){}}{}[])]})
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backtick... | {
"game_data": {
"answer": "({[({({([({{}{}}()[])][])}){}}{}[])]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "({[({({([({{}{}}()[])][])}){}}{}[])]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[({({([({{",
... |
logic-v2 | Fill in the blank:
_____ + ⦆⟦⟧)⦃⦄⟦⟧]⟧>)⦄}>>⟧]⟩⟩⟧)>⟩⦆]⦆⦄ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦅[⦅⟨<(⟦⟨⟨[⟦<<{⦃(<⟦[(⦅⦆⟦⟧)⦃⦄⟦⟧]⟧>)⦄}>>⟧]⟩⟩⟧)>⟩⦆]⦆⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"full_sequence": "⦃⦅[⦅⟨<(⟦⟨⟨[⟦<<{⦃(<⟦[(⦅⦆⟦⟧)⦃⦄⟦⟧]⟧>)⦄}>>⟧]⟩⟩⟧)>⟩⦆]⦆⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: )<>()⟩}{}]>{}<>{}]}}⟩)>}}>]}⟩}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{⟨{[<{{<(⟨{{[<[{⟨()<>()⟩}{}]>{}<>{}]}}⟩)>}}>]}⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "{⟨{[<{{<(⟨{{[<[{⟨()<>()⟩}{}]>{}<>{}]}}⟩)>}}>]}⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{... |
logic-v2 | Q: What opening brackets should precede "⦄}]()⟦⟧" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{⦃⦄}]()⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "[{⦃⦄}]()⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[{⦃",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 1816... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"<>>[]>{}{})}{}]]{}}>{}}])()]>>()]()}]<>]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence)... | {
"game_data": {
"answer": "[[{[<<[([{<{[[{(<<<>>[]>{}{})}{}]]{}}>{}}])()]>>()]()}]<>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "[[{[<<[([{<{[[{(<<<>>[]>{}{})}{}]]{}}>{}}])()]>>()]()}]<>]",
"n_types": 4,
"nesting_depth": 0,
... |
logic-v2 | Let S = "⟦⟧⟦⟧⦄⦄⟧⟩>⟩}⟩>⟧⟧]⟨⟩⦅⦆{}⟨⟩{}⦃⦄⦅⦆⦅⦆()⦅⦆⦅⦆" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[⟦⟦<⟨{⟨<⟨⟦⦃⦃⟦⟧⟦⟧⦄⦄⟧⟩>⟩}⟩>⟧⟧]⟨⟩⦅⦆{}⟨⟩{}⦃⦄⦅⦆⦅⦆()⦅⦆⦅⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[⟦⟦<⟨{⟨<⟨⟦⦃⦃⟦⟧⟦⟧⦄⦄⟧⟩>⟩}⟩>⟧⟧]⟨⟩⦅⦆{}⟨⟩{}⦃⦄⦅⦆⦅⦆()⦅⦆⦅⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: }⟧⟧]⟧]>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<[⟦[⟦⟦{}⟧⟧]⟧]>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "<[⟦[⟦⟦{}⟧⟧]⟧]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[⟦[⟦⟦{",
"prompt_name": "puzzle",
"prompt_variant": 2,
... |
logic-v2 | Fill in the blank:
_____ + <>⟩⟧]⟧]⟩)]>>}> = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<{<<[(⟨[⟦[⟦⟨<>⟩⟧]⟧]⟩)]>>}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "<{<<[(⟨[⟦[⟦⟨<>⟩⟧]⟧]⟩)]>>}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{<<[(⟨[⟦[⟦⟨",
"prompt_name": "fill_in"... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟩>⟨⟩)]}⦆<>]()}){}[]⦃⦄⟨⟩⟨⟩(){}⟦⟧⦅⦆<>{}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) ... | {
"game_data": {
"answer": "({[⦅{[(<⟨⟩>⟨⟩)]}⦆<>]()}){}[]⦃⦄⟨⟩⟨⟩(){}⟦⟧⦅⦆<>{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "({[⦅{[(<⟨⟩>⟨⟩)]}⦆<>]()}){}[]⦃⦄⟨⟩⟨⟩(){}⟦⟧⦅⦆<>{}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "({[⦅{[... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: >{}>})[])])]⟩}{}()(){}{}()[]()()()
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not... | {
"game_data": {
"answer": "{⟨[([(({<<>{}>})[])])]⟩}{}()(){}{}()[]()()()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "{⟨[([(({<<>{}>})[])])]⟩}{}()(){}{}()[]()()()",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨[([(({<... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: <>>⟨⟩[]⟧⟦⟧⟩⟧)>⟦⟧})]{}⟩>[]⟨⟩[][]
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide y... | {
"game_data": {
"answer": "<⟨[({<(⟦⟨⟦<<>>⟨⟩[]⟧⟦⟧⟩⟧)>⟦⟧})]{}⟩>[]⟨⟩[][]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "<⟨[({<(⟦⟨⟦<<>>⟨⟩[]⟧⟦⟧⟩⟧)>⟦⟧})]{}⟩>[]⟨⟩[][]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨[({<(⟦⟨⟦<",... |
logic-v2 | Fill in the blank:
_____ + ⟧⦅⦆]⦆⦆] = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[⦅⦅[⟦⟧⦅⦆]⦆⦆]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[⦅⦅[⟦⟧⦅⦆]⦆⦆]",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[⦅⦅[⟦",
"prompt_name": "fill_in",
"prompt_variant": 7,
"... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ())]⟩⟦⟧⟦⟧()⦃⦄{}
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer... | {
"game_data": {
"answer": "⟨[(())]⟩⟦⟧⟦⟧()⦃⦄{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "⟨[(())]⟩⟦⟧⟦⟧()⦃⦄{}",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[(",
"prompt_name": "reverse_perspective",
"promp... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: >)⟧⟩]⟩⦃⦄
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the c... | {
"game_data": {
"answer": "⟨[⟨⟦(<>)⟧⟩]⟩⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⟨[⟨⟦(<>)⟧⟩]⟩⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟨⟦(<",
"prompt_name": "reverse_perspective",
"prompt_var... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟨⟩[]{}><>>⟨⟩[]<>{})()<>}()<>⟩})]⟩}
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provid... | {
"game_data": {
"answer": "{⟨[({⟨{(<<⟨⟩[]{}><>>⟨⟩[]<>{})()<>}()<>⟩})]⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "{⟨[({⟨{(<<⟨⟩[]{}><>>⟨⟩[]<>{})()<>}()<>⟩})]⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨[({⟨{(<... |
logic-v2 | Q: What opening brackets should precede ")()><>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<()()><>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "<()()><>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 133227813... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ))()[][]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pai... | {
"game_data": {
"answer": "(())()[][]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "(())()[][]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 1... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟩⟩⟩⦅⦆⟧⦆[]>⟦⟧⟩⟧}⦄⟧
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `a... | {
"game_data": {
"answer": "⟦⦃{⟦⟨<⦅⟦⟨⟨⟨⟩⟩⟩⦅⦆⟧⦆[]>⟦⟧⟩⟧}⦄⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟦⦃{⟦⟨<⦅⟦⟨⟨⟨⟩⟩⟩⦅⦆⟧⦆[]>⟦⟧⟩⟧}⦄⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦⦃{⟦⟨<⦅⟦⟨⟨⟨",
"prompt_name": "puzzl... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: []⟩]()⟩⟦⟧]}{}>[]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `an... | {
"game_data": {
"answer": "<{[⟨[⟨[]⟩]()⟩⟦⟧]}{}>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "<{[⟨[⟨[]⟩]()⟩⟦⟧]}{}>[]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{[⟨[⟨",
"prompt_name": "puzzle",
"prompt_... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: )⟧[]{}⟩⟩()⦄⟦⟧⦄)>⦆⟧⦄⟩]⟧})⦄⟧)⟧
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add a... | {
"game_data": {
"answer": "⟦(⟦⦃({⟦[⟨⦃⟦⦅<(⦃⦃⟨⟨⟦()⟧[]{}⟩⟩()⦄⟦⟧⦄)>⦆⟧⦄⟩]⟧})⦄⟧)⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "⟦(⟦⦃({⟦[⟨⦃⟦⦅<(⦃⦃⟨⟨⟦()⟧[]{}⟩⟩()⦄⟦⟧⦄)>⦆⟧⦄⟩]⟧})⦄⟧)⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦... |
logic-v2 | A sequence of brackets was cut, and only the end remains:
">}>)}>][][]<>>]}<>)})])>})]>}>]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backt... | {
"game_data": {
"answer": "[<{<[({<([({({[<[<{(<{<>}>)}>][][]<>>]}<>)})])>})]>}>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "[<{<[({<([({({[<[<{(<{<>}>)}>][][]<>>]}<>)})])>})]>}>]",
"n_types": 4,
"nesting_depth": 0,
"opening... |
logic-v2 | Let S = ")⟨⟩{}{})<>⦅⦆]⟩)⦄[]]⟧]⦅⦆⟦⟧⦅⦆{}⦃⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[⟦[⦃(⟨[(()⟨⟩{}{})<>⦅⦆]⟩)⦄[]]⟧]⦅⦆⟦⟧⦅⦆{}⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[⟦[⦃(⟨[(()⟨⟩{}{})<>⦅⦆]⟩)⦄[]]⟧]⦅⦆⟦⟧⦅⦆{}⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "[⟦[⦃(⟨[((",
... |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: }}]})]))}))})}]])})
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like ... | {
"game_data": {
"answer": "({([[{({(({(([({[{{}}]})]))}))})}]])})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "({([[{({(({(([({[{{}}]})]))}))})}]])})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({([[{({(({(([({[{{",... |
logic-v2 | Let S = ">)[][]]{}>}}[]⟨⟩()}<>]>()>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "<<[{{{<[(<>)[][]]{}>}}[]⟨⟩()}<>]>()>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<<[{{{<[(<>)[][]]{}>}}[]⟨⟩()}<>]>()>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<[{{{<[(<",
"promp... |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ))})})]}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pai... | {
"game_data": {
"answer": "{[({({(())})})]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "{[({({(())})})]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[({({((",
"prompt_name": "direct",
"prompt_variant": ... |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟩⟩[]()⟦⟧))]}}⟩>⟩))⟧)}⟩>))>⟧>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your... | {
"game_data": {
"answer": "<⟦<((<⟨{(⟦((⟨<⟨{{[((⟨⟨⟩⟩[]()⟦⟧))]}}⟩>⟩))⟧)}⟩>))>⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"full_sequence": "<⟦<((<⟨{(⟦((⟨<⟨{{[((⟨⟨⟩⟩[]()⟦⟧))]}}⟩>⟩))⟧)}⟩>))>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix"... |
logic-v2 | Let S = "<>()}}{}<>⟧}⦄}⟩⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨{⦃{⟦{{<>()}}{}<>⟧}⦄}⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⦃⟨{⦃{⟦{{<>()}}{}<>⟧}⦄}⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨{⦃{⟦{{",
"prompt_name": "mathematical",
... |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]]⟧]⟩⦄⦄
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦃⟨[⟦[[]]⟧]⟩⦄⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⦃⦃⟨[⟦[[]]⟧]⟩⦄⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟨[⟦[[",
"prompt_name": "technical",
"prompt_variant": 3,... |
logic-v2 | Fill in the blank:
_____ + ⦃⦄⦅⦆⟧>⦆⟧⟧>>⦆⦄⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⦃⦅<<⟦⟦⦅<⟦⦃⦄⦅⦆⟧>⦆⟧⟧>>⦆⦄⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "⟨⦃⦅<<⟦⟦⦅<⟦⦃⦄⦅⦆⟧>⦆⟧⟧>>⦆⦄⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨⦃⦅<<⟦⟦⦅<⟦",
"prompt_name": "fill_in",
... |
logic-v2 | Let S = "⟧){}⦄}<>]<>[]]⦄[]⦃⦄]⦃⦄]>⟧⟧⟧])}])}}⦄⟩⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⦃{{([{([⟦⟦⟦<[[⦃[[{⦃(⟦⟧){}⦄}<>]<>[]]⦄[]⦃⦄]⦃⦄]>⟧⟧⟧])}])}}⦄⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "⦃⟨⦃{{([{([⟦⟦⟦<[[⦃[[{⦃(⟦⟧){}⦄}<>]<>[]]⦄[]⦃⦄]⦃⦄]>⟧⟧⟧])}])}}⦄⟩⦄",
"n_types": 7,
"nesting_depth": 0,
... |
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