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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": 9, "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": 5, "full_sequence": "⟦(⦃{⦅⦆()}⦄)⟧(){}⟦⟧[]⟦⟧⟦⟧{}", "n_types": 8, "nesting_depth": 0, "opening_prefix": "⟦(⦃{⦅", "prompt_name": "qa", "prom...
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 (t...
{ "game_data": { "answer": "[{((([[{(<<()>>)}]])))}]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 12, "full_sequence": "[{((([[{(<<()>>)}]])))}]", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[{((([[{(<<(", "prompt_name": "reverse_pers...
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": 28, "full_sequence": "⟨⟦<⦅{⟦{{⟨{[⦃⟦⟦⟨⦃{{{⟨⦅⦅[<[⟦(⦃⦄)⟧⟨⟩⦅⦆]>]⦆⦆⟩}}}⦄⟩⟧⟧⦄]}⟩}}⟧}⦆>⟧⟩", "n_types": 8, "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": 2, "full_sequence": "{()}(){}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{(", "prompt_name": "mathematical", "prompt_variant": 5, "seed":...
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 ext...
{ "game_data": { "answer": "[<<([<<(([([(<()><>)][]())]))>>])>>]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 14, "full_sequence": "[<<([<<(([([(<()><>)][]())]))>>])>>]", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[<<([<<(([([(<", "p...
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": 24, "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 backti...
{ "game_data": { "answer": "({{[[{[[([{[{[({[[()][]]}()())[]{}]}]}])]]}]]}})", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 18, "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": 2, "full_sequence": "{()()⟨⟩{}}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{(", "prompt_name": "mathematical", "prompt_variant": 5, "se...
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, "s...
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": 12, "full_sequence": "{(<⟨{<(<⟨[<([])>]⟩<>()>[]()⟨⟩)>}⟩>)}{}⟨⟩{}{}{}<>", "n_types": 5, "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 bra...
{ "game_data": { "answer": "⟨<⟦([⟦[({⟨[[⟨{{⟨⟩}}⟩]]⟩})]⟧])⟧>⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 16, "full_sequence": "⟨<⟦([⟦[({⟨[[⟨{{⟨⟩}}⟩]]⟩})]⟧])⟧>⟩", "n_types": 7, "nesting_depth": 0, "opening_prefix": "⟨<⟦([⟦[({⟨[[⟨{{⟨", "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 any extr...
{ "game_data": { "answer": "{⟨⟨({({{{{<[(<<⟨{{⟨⟩}}⟩>⟨⟩>)]>}}}})})⟩⟩}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 19, "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 your final an...
{ "game_data": { "answer": "⟨{⟦(()[]){}()⟧[]}⟩{}[]{}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 5, "full_sequence": "⟨{⟦(()[]){}()⟧[]}⟩{}[]{}", "n_types": 7, "nesting_depth": 0, "opening_prefix": "⟨{⟦((", "prompt_name": "reverse_perspective"...
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": 3, "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 sequence) in backticks lik...
{ "game_data": { "answer": "⟨<{[[{⦃⟨⟨⟦⟦⟧⟧⟩⟨⟩⦃⦄⟩<>⟦⟧⦄}⟦⟧]]}>⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 11, "full_sequence": "⟨<{[[{⦃⟨⟨⟦⟦⟧⟧⟩⟨⟩⦃⦄⟩<>⟦⟧⦄}⟦⟧]]}>⟩", "n_types": 7, "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": 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 f...
{ "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": 7, "full_sequence": "<⟨[⦃[(()⟨⟩)]⦄]⟩()>", "n_types": 8, "nesting_depth": 0, "opening_prefix": "<⟨[⦃[((", "prompt_name": "story", "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": 13, "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 backticks li...
{ "game_data": { "answer": "<⟨{(⟦<({[<⟨<[{[[{<<⟦⟧>>}]]⟦⟧}]()>⟩>]})>⟧)}⟩>", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 20, "full_sequence": "<⟨{(⟦<({[<⟨<[{[[{<<⟦⟧>>}]]⟦⟧}]()>⟩>]})>⟧)}⟩>", "n_types": 6, "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 `answe...
{ "game_data": { "answer": "((([([]())])))[]{}[]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 5, "full_sequence": "((([([]())])))[]{}[]", "n_types": 3, "nesting_depth": 0, "opening_prefix": "((([(", "prompt_name": "story", "prompt_varian...
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": 21, "full_sequence": "⟨⦃{[<{⦃{(⟦(⟨<[{((⟨(⦃()⦄)()⦃⦄⟩))⟦⟧[]}]>()⦃⦄()⟩)⟧⟨⟩)}[]⦄}>]}⦄⟩", "n_types": 7, "nesting_depth": 0, ...
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": 5, "full_sequence": "⟨[<[⦃⦄]>⟨⟩]{}⟩", "n_types": 7, "nesting_depth": 0, "opening_prefix": "⟨[<[⦃", "prompt_name": "puzzle", "prompt_variant": 2, ...
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 ...
{ "game_data": { "answer": "{{(⟨⟩⟦⟧{}<>)}}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 3, "full_sequence": "{{(⟨⟩⟦⟧{}<>)}}", "n_types": 8, "nesting_depth": 0, "opening_prefix": "{{(", "prompt_name": "direct", "prompt_variant": 0, ...
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": 8, "full_sequence": "{⟨<{⦅⦅⦃⦃⦄⦄⦆⦆}>⟩}", "n_types": 8, "nesting_depth": 0, "opening_prefix": "{⟨<{⦅⦅⦃⦃", "prompt_name": "story", "prompt_variant": 4...
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": 22, "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 ...
{ "game_data": { "answer": "⟦⟨((⦃⟨(⦅<⟨[⦅<[⦅⦃{{⦃([⟨<>⟩])⦄<>}}⦄(){}⦆]⦅⦆><>⦆]⟩⦅⦆>⦆)⟩⦄))⟩⟧", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 22, "full_sequence": "⟦⟨((⦃⟨(⦅<⟨[⦅<[⦅⦃{{⦃([⟨<>⟩])⦄<>}}⦄(){}⦆]⦅⦆><>⦆]⟩⦅⦆>⦆)⟩⦄))⟩⟧", "n_types": 8, "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": 12, "full_sequence": "{⟨{⟨<<(<{{<⟨{}()()⟩>}}>{}⟨⟩)>⟨⟩>⟩{}[]()}⟩}", "n_types": 5, "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 ...
{ "game_data": { "answer": "[({(((<{[{{{<({<{{((<<>><>))}}>})>}}}]}>)))})]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 21, "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 (...
{ "game_data": { "answer": "([{[{(([[]]){})}()]}])", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 9, "full_sequence": "([{[{(([[]]){})}()]}])", "n_types": 3, "nesting_depth": 0, "opening_prefix": "([{[{(([[", "prompt_name": "reverse_perspective"...
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...
{ "game_data": { "answer": "<⟦⟦⟨([⟨{[[(⟦⟦[⟦[{<<[]{}⟨⟩()>>}]⟧]⟧⟧)]]}⟩])⟩⟧⟧>", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 20, "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": 4, "full_sequence": "(([[]]))", "n_types": 3, "nesting_depth": 0, "opening_prefix": "(([[", "prompt_name": "mathematical", "prompt_variant": 5, "seed...
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": 5, "full_sequence": "{[{⟨<>[]⟩}]}[]{}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{[{⟨<", "prompt_name": "qa", "prompt_variant": 6, ...
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": 3, "nesting_depth": 0, "opening_prefix": "(({({([{{", "prompt_name": "technical", "promp...
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": 3, "nesting_depth": 0, "opening_prefix": "([{[({(({", "prompt_name": "technical", ...
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 bac...
{ "game_data": { "answer": "({{<⦃⦃⦃⦄⦄[]⦄⟨⟩⦅⦆>⦃⦄[]}}⟨⟩)⟦⟧⦅⦆{}⟨⟩⟨⟩[]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 7, "full_sequence": "({{<⦃⦃⦃⦄⦄[]⦄⟨⟩⦅⦆>⦃⦄[]}}⟨⟩)⟦⟧⦅⦆{}⟨⟩⟨⟩[]", "n_types": 8, "nesting_depth": 0, "opening_prefix": "({{<⦃⦃⦃", "promp...
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": 15, "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 se...
{ "game_data": { "answer": "<([⟦⟨⟦[⟦<(([(())⟦⟧]{})⟨⟩{})>⟧⟨⟩]⟧⟩<>⟧⟦⟧{}]){}>⟨⟩⟦⟧{}<>[]⟨⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 13, "full_sequence": "<([⟦⟨⟦[⟦<(([(())⟦⟧]{})⟨⟩{})>⟧⟨⟩]⟧⟩<>⟧⟦⟧{}]){}>⟨⟩⟦⟧{}<>[]⟨⟩", "n_types": 6, "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 final answe...
{ "game_data": { "answer": "<{[(⟦[]⟧⟨⟩)]{}}>()[]⟦⟧", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 6, "full_sequence": "<{[(⟦[]⟧⟨⟩)]{}}>()[]⟦⟧", "n_types": 6, "nesting_depth": 0, "opening_prefix": "<{[(⟦[", "prompt_name": "reverse_perspective", ...
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...
{ "game_data": { "answer": "(([(())[]])){}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 4, "full_sequence": "(([(())[]])){}", "n_types": 3, "nesting_depth": 0, "opening_prefix": "(([(", "prompt_name": "reverse_perspective", "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": 11, "full_sequence": "[<{{[([<<(())<>>>]())]{}}<>[]()}>]", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[<{{[([<<((", "prompt_n...
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": 9, "full_sequence": "{<[<[{⟨⟨()[][]⟩⟩}]>]>}{}()⟨⟩⟨⟩⟨⟩", "n_types": 5, "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": 24, "full_sequence": "<<<<[(⟦⟦⟨(⟦[{{⟨[⟨(<(<{(<>)[]⟦⟧[]}⟨⟩>)>)⟩]⟩}}]⟧)⟩⟧⟧)]>>>>", "n_types": 6, "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": 5, "full_sequence": "(([[()]]))", "n_types": 3, "nesting_depth": 0, "opening_prefix": "(([[(", "prompt_name": "story", "prompt_variant": 4, "seed":...
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 ext...
{ "game_data": { "answer": "[<<(<{(<<{{()}}>>)}<>>)[]>>()][]<>", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 12, "full_sequence": "[<<(<{(<<{{()}}>>)}<>>)[]>>()][]<>", "n_types": 4, "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 se...
{ "game_data": { "answer": "⟨⦃(⟦⟦⟨{{⦃(⟦⟧())⦄<>}}⟩⟧⟧){}⦄⟩⟨⟩⦃⦄{}[]⟦⟧⟨⟩⟨⟩()⟦⟧{}<>⦃⦄⟨⟩[]⟦⟧", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 11, "full_sequence": "⟨⦃(⟦⟦⟨{{⦃(⟦⟧())⦄<>}}⟩⟧⟧){}⦄⟩⟨⟩⦃⦄{}[]⟦⟧⟨⟩⟨⟩()⟦⟧{}<>⦃⦄⟨⟩[]⟦⟧", "n_types": 7, "nesting_depth": 0, ...
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 ...
{ "game_data": { "answer": "([([[([{{(){}()}()}])][]{}])])[]{}{}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 10, "full_sequence": "([([[([{{(){}()}()}])][]{}])])[]{}{}", "n_types": 3, "nesting_depth": 0, "opening_prefix": "([([[([{{(", "promp...
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": 3, "nesting_depth": 0, "opening_prefix": "((", "prompt_name": "technical", "prompt_variant": 3, "seed": 17...
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": 8, "nesting_depth": 0, "opening_prefix": "<⦅⟨{⦃[[", "prompt_name": "fill_in", "prompt_varian...
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", ...
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": 2, "full_sequence": "((())()){}", "n_types": 3, "nesting_depth": 0, "opening_prefix": "((", "prompt_name": "fill_in", "prompt_variant": 7, "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": 18, "full_sequence": "⟨⦅⦃⟦⟨{<<⦅⟦<<<⦅<[<⦃⦄<>>]⟨⟩()⦃⦄>⦆>>><>⟧⦆⦃⦄>>}⟩⟧⦄⦆⟩", "n_types": 8, "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": 17, "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",...
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": 6, "nesting_depth": 0, "opening_prefix": "<(", "prompt_name": "story", "prompt_variant": 4, "seed": 121565183,...
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": 6, "nesting_depth": 0, "opening_prefix": "<{(<((", "prompt_name": "qa", ...
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": 19, "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": 11, "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": 16, "full_sequence": "[{<([<[<([([[<[{}]()>]])()])>{}]>])>}]", "n_types": 4, "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 `a...
{ "game_data": { "answer": "⟨<{<{⟨⟨⟨⟩⟩⟩()}>⟨⟩(){}}>⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 7, "full_sequence": "⟨<{<{⟨⟨⟨⟩⟩⟩()}>⟨⟩(){}}>⟩", "n_types": 8, "nesting_depth": 0, "opening_prefix": "⟨<{<{⟨⟨", "prompt_name": "puzzle", "pr...
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": 5, "nesting_depth": 0, "opening_prefix": "{[<<({[", "prompt_name": "fill_in", "prompt_va...
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": 3, "nesting_depth": 0, "opening_prefix": "([(({(", "prompt_name": "puzzle", "prompt_...
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": 15, "full_sequence": "[<<{[[({(<((([[]<>])))>)})]]}>>]", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[<<{[[({(<((([[", "prompt_n...
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...
{ "game_data": { "answer": "[<(({<[]>})[][]<>)<><>>[]][](){}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 6, "full_sequence": "[<(({<[]>})[][]<>)<><>>[]][](){}", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[<(({<", "prompt_name": "dir...
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": 15, "full_sequence": "<<⟨{[<(((⟦<<⟨⟦<>{}⟧⟩>>⟨⟩⟧)))>]}⟩>>", "n_types": 6, "nesting_depth": 0, "opening_prefix": "<<⟨{[<(((⟦<<⟨⟦<", "prom...
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": 14, "full_sequence": "<([⟨(([{[<<<<⟨[]⟩>>>()>]}]))⟦⟧⟩][])⟨⟩>()⟦⟧⟦⟧⟨⟩[](){}[]⟨⟩", "n_types": 6, "nesting_depth": 0, "ope...
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": 16, "full_sequence": "{<<{(<⟨(<⟨{{{<(⟨⟩)>}}}⟩>)⟩>)}>>}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{<<{(<⟨(<⟨{{{<(⟨", "prompt_...
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": 4, "full_sequence": "<(⟨⟨⟩⟩)>", "n_types": 6, "nesting_depth": 0, "opening_prefix": "<(⟨⟨", "prompt_name": "fill_in", "prompt_variant": 7, "seed": 11...
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...
{ "game_data": { "answer": "({[[({[[{{[{}]}}]{}]}())]{}]{}}[])()[]", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 11, "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": 14, "full_sequence": "<⟨<{<⟨<[⟦<⟨(⟨⟦<>⟧<>⟩)⟩>⟧⟨⟩<>]>⟩⟨⟩[]>}[]>⟩>⟦⟧", "n_types": 6, "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) ...
{ "game_data": { "answer": "<{⟨[⟦<<([(((⟨{[[(([⟨{(⟦⟧[])}⟩]))]]}⟩)){})]⟦⟧)>>⟧[]]⟩}<>()>⟨⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 23, "full_sequence": "<{⟨[⟦<<([(((⟨{[[(([⟨{(⟦⟧[])}⟩]))]]}⟩)){})]⟦⟧)>>⟧[]]⟩}<>()>⟨⟩", "n_types": 6, "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 final ...
{ "game_data": { "answer": "{{(⟨(<>⟨⟩)⟩)<>()}}()⟨⟩{}<>", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 5, "full_sequence": "{{(⟨(<>⟨⟩)⟩)<>()}}()⟨⟩{}<>", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{{(⟨(", "prompt_name": "reverse_perspect...
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 a...
{ "game_data": { "answer": "<⟨((⟨<[{}]⟨⟩>⟩){})()⟩<>>⟦⟧[][]⟨⟩⟨⟩{}⟦⟧{}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 8, "full_sequence": "<⟨((⟨<[{}]⟨⟩>⟩){})()⟩<>>⟦⟧[][]⟨⟩⟨⟩{}⟦⟧{}", "n_types": 6, "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 b...
{ "game_data": { "answer": "([[[({[([[((({(({{([[{{}[]}]]{})}}){})}{}))){}{}]])]})]]])", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 23, "full_sequence": "([[[({[([[((({(({{([[{{}[]}]]{})}}){})}{}))){}{}]])]})]]])", "n_types": 3, "nesting_depth": 0, ...
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": 6, "nesting_depth": 0, "ope...
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": 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": 4, "full_sequence": "(({[()]}))", "n_types": 3, "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 sequence) in backticks like...
{ "game_data": { "answer": "⟨({<<>⟨⟩>}⦃⦄()<>⦃⦄)⟩<>⦃⦄", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 4, "full_sequence": "⟨({<<>⟨⟩>}⦃⦄()<>⦃⦄)⟩<>⦃⦄", "n_types": 8, "nesting_depth": 0, "opening_prefix": "⟨({<", "prompt_name": "puzzle", "promp...
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": 26, "full_sequence": "⟨⦃<<⟨⟨(⟦⟦⟨[[⟦(⟨<⦃(⟨⟨<⦃<⟨⦃⦃⦄⦄{}⟩>⦄>⟩⟩)⦄⦃⦄>⟩)⟧[]]]⟩⟧⟧)⟩⟩>>⦄⟩", "n_types": 7, "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": 1, "full_sequence": "({}[]){}", "n_types": 3, "nesting_depth": 0, "opening_prefix": "(", "prompt_name": "technical", "prompt_variant": 3, "seed": 146...
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": 16, "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": 22, "full_sequence": "⟨⦃{⦃⦃{{<{{([([⟨{⟨⟨⦃[<<><>>(){}<>{}<>{}]⦄⟩⟩}⟩])])}}>}}⦄⦄}⦄⟩", "n_types": 7, "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": 17, "full_sequence": "[[{[{[{{[[[[[[({()})]]]]][]]}()}]}[]]()}]()]()[][]", "n_types": 4, "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": 10, "full_sequence": "{{{<<[([⟨[]()⟩()⟨⟩])]>>}}}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{{{<<[([⟨[", "prompt_name": "qa", ...
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": 19, "full_sequence": "({{[(([{[{({(([([[([])]{}])]{}))()})}]}]))]}})", "n_types": 3, "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 you...
{ "game_data": { "answer": "⟦[⟨⟨⦅⦃⦅(([{⟦⟨⟦[{⦃<⦃[[()]<>()]⟨⟩⦄>⦄}]⟧⟩⟧}]))⦆⦄⦆⟩⟩]⟧", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 21, "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": 12, "full_sequence": "([[{(([{({[(){}]()}[]{}[])}]))}]])", "n_types": 3, "nesting_depth": 0, "opening_prefix": "([[{(([{({[(", "prompt_...
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": 4, "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 bracket p...
{ "game_data": { "answer": "<[(⟨⟨(<(⟦<>⟧)>)⟩⟩)]>", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 10, "full_sequence": "<[(⟨⟨(<(⟦<>⟧)>)⟩⟩)]>", "n_types": 6, "nesting_depth": 0, "opening_prefix": "<[(⟨⟨(<(⟦<", "prompt_name": "direct", "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 `answer`...
{ "game_data": { "answer": "{[<{⟨[<>]⟩}()>{}⟨⟩]}", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 7, "full_sequence": "{[<{⟨[<>]⟩}()>{}⟨⟩]}", "n_types": 5, "nesting_depth": 0, "opening_prefix": "{[<{⟨[<", "prompt_name": "story", "prompt_vari...
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, "see...
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": 6, "nesting_depth": 0, "opening_prefix": "<[<{⟨(⟨", "prompt_name": "story", "prompt_vari...
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 l...
{ "game_data": { "answer": "⟨⟨<⦃{{[{⟦((<⟦⟧>⦃⦄))<>[]⟧{}}()()]}}⦄>⟩⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 13, "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": 8, "full_sequence": "⟨[⟦<{⟨⟦⦃⦄⟧⟩}>⟧]⟩", "n_types": 7, "nesting_depth": 0, "opening_prefix": "⟨[⟦<{⟨⟦⦃", "prompt_name": "qa", "prompt_variant": 6, ...
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": 20, "full_sequence": "<{<<(⟦⟨(<⟨{<<(⟦<⟨[[()]]⟩>[]<>⟧)[]><>>⟦⟧}{}⟩()><>⟨⟩)⟩⟧)>>}>", "n_types": 6, "nesting_depth": 0, ...
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": 9, "full_sequence": "[{{<{{[({})][][]}[]}>}}]", "n_types": 4, "nesting_depth": 0, "opening_prefix": "[{{<{{[({", "prompt_name": "fill_in", ...
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 Pleas...
{ "game_data": { "answer": "[[<⟦⟦⟦[⦃[⦅⦃([{}<>])⦄⦃⦄⦆]⦃⦄{}⦅⦆()⦄{}][]⟨⟩⟧⟧()⟧>()]][]<>⟨⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 14, "full_sequence": "[[<⟦⟦⟦[⦃[⦅⦃([{}<>])⦄⦃⦄⦆]⦃⦄{}⦅⦆()⦄{}][]⟨⟩⟧⟧()⟧>()]][]<>⟨⟩", "n_types": 8, "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 extra bracket pairs...
{ "game_data": { "answer": "⟨(⟨⟨⟨⦃⦄⟩⟩⟩)⟩", "difficulty": 1, "gpt_response": "", "metadata": { "fill_length": 6, "full_sequence": "⟨(⟨⟨⟨⦃⦄⟩⟩⟩)⟩", "n_types": 7, "nesting_depth": 0, "opening_prefix": "⟨(⟨⟨⟨⦃", "prompt_name": "direct", "prompt_variant": 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": 6, "full_sequence": "⦃(⟦<(⟨⟩)>⟧)()⦄<>⟨⟩⦅⦆⦅⦆{}[]⦅⦆<>", "n_types": 8, "nesting_depth": 0, "opening_prefix": "⦃(⟦<(⟨", "prompt_name": "mathema...