env stringclasses 1
value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
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": 14,
"full_sequence": "([{{([{([({({[]}{}){}})])}])}}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{{([{([({({[",
"prompt_na... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[[(",
"prompt_name": "mathematical",
"prompt_variant":... |
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": 8,
"nesting_depth": 0,
"opening_prefix": "<⦅⟨⟨(⟦",
"prompt_name": "story",
"prompt_variant":... |
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": 8,
"nesting_depth": 0,
"opening_prefix": "⟨⟦⦅{⟦⟦[{(",
"prompt_name": "fill_in",
"pro... |
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": 7,
"full_sequence": "(([{[[[]()][][]]}]))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([{[[[",
"prompt_name": "qa",
"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": 3,
"full_sequence": "(⟨⟦⟧⟩)⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟨⟦",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed"... |
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 sequen... | {
"game_data": {
"answer": "{({<(([[<<([[]]<>)>>]]()))>}<>)(){}()}⟨⟩[]⟨⟩[]<>{}()()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "{({<(([[<<([[]]<>)>>]]()))>}<>)(){}()}⟨⟩[]⟨⟩[]<>{}()()<>",
"n_types": 5,
"nesting_depth": 0,
"ope... |
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": 6,
"full_sequence": "⟨{[⟨⦃[<>]⦃⦄<>⦄⟩⟨⟩⟦⟧]{}}⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{[⟨⦃[",
"prompt_name": "puzzle",
"pro... |
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": 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": 4,
"full_sequence": "{⟦⟦{<>}⟧⟧()}<>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{⟦⟦{",
"prompt_name": "mathematical",
"prompt_variant": 5,... |
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 pro... | {
"game_data": {
"answer": "{[((⟨{<{⟨⟨<⟨[⟨⟨⟨<>()()⟨⟩[]⟩{}⟩⟩]⟩[][]>⟩⟩}>}⟩))]<>}<>()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "{[((⟨{<{⟨⟨<⟨[⟨⟨⟨<>()()⟨⟩[]⟩{}⟩⟩]⟩[][]>⟩⟩}>}⟩))]<>}<>()",
"n_types": 5,
"nesting_depth": 0,
"opening... |
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": 23,
"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 backtick... | {
"game_data": {
"answer": "⟨⟨⦃⦃{⦃[{(⦃[⟨⟩[]]⦄)()}⟦⟧]⦄{}}⦄{}()⟦⟧⦄⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"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 b... | {
"game_data": {
"answer": "{⟨[⟨<⟨⟨([⦅⦃⟦⟨()⟩⟧⦄<>⦃⦄⦅⦆⦆])⦅⦆⟩{}⟩>⟩]<>⟩}⟨⟩[]⦅⦆{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"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... | {
"game_data": {
"answer": "{<{[<[⟨{(⟨<{}>⟩)⟨⟩{}}⟩]>]}>}<><>⟨⟩{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "{<{[<[⟨{(⟨<{}>⟩)⟨⟩{}}⟩]>]}>}<><>⟨⟩{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<{[<[⟨{(⟨<",
"prom... |
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 ba... | {
"game_data": {
"answer": "[{[<(<{{<[[()[][]]<>()]>{}}}>{})>[]<>]}<><>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "[{[<(<{{<[[()[][]]<>()]>{}}}>{})>[]<>]}<><>]",
"n_types": 4,
"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": 26,
"full_sequence": "{⟨<{(⟨⟨[[<([<⟨([<{<{<⟨<⟨{[]}⟩>⟩>}>}>])⟩>])>]]⟩⟩)}>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_pre... |
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": 8,
"nesting_depth": 0,
"opening_prefix": "⦅⦅⟦[⟦⟦⦃⟨<⦃(⟨⦅",
"prompt... |
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": 13,
"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": 4,
"full_sequence": "⟨[⦃⦃()⟨⟩⦄⦃⦄⦄]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⦃⦃",
"prompt_name": "qa",
"prompt_variant": 6,
"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": 3,
"nesting_depth": 0,
"opening_prefix": "((",
"prompt_name": "technical",
"prompt_variant": 3,
"seed"... |
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": 8,
"full_sequence": "<[⟦⟨⟦⟦[⟦⟧⟦⟧]⟧⟧⟩⟧]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<[⟦⟨⟦⟦[⟦",
"prompt_name": "puzzle",
"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) in backticks ... | {
"game_data": {
"answer": "[[[<<<<((({([<[{{}{}{}<>}]>])})))>>>>]]]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"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 (t... | {
"game_data": {
"answer": "<{<⟦⟨([⟦<<⟦⟧>>⟧])⟩⟧>}>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<{<⟦⟨([⟦<<⟦⟧>>⟧])⟩⟧>}>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{<⟦⟨([⟦<<",
"prompt_name": "reverse_perspectiv... |
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 lik... | {
"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 | [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": 4,
"nesting_depth": 0,
"opening_prefix": "[{([{",
"prompt_name": "technical",
"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... | {
"game_data": {
"answer": "<⟨[(⟨{{([()])}}⟩){}<>]<>⟦⟧⟦⟧⟩[]<>><>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<⟨[(⟨{{([()])}}⟩){}<>]<>⟦⟧⟦⟧⟩[]<>><>[]",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨[(⟨{{([(",
"p... |
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": 28,
"full_sequence": "⟨⦃⟨(<⟦⦃<(<([⦃[[[⟦⟦([⟨⟦⟨(⦃⦃<{<>[]}>⦄⦄)⟩⟧⟩])⟧⟧]]]⦄])>)>⦄⟧>)⟩⦄⟩",
"n_types": 7,
"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": 14,
"full_sequence": "({[{[(([[[({{()()}})]]()]))]}]}{}){}()",
"n_types": 3,
"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": 14,
"full_sequence": "[<(<{<[[[[(<<[[]]{}>>)]]]]>}>)>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<(<{<[[[[(<<[",
"prompt_na... |
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": 9,
"full_sequence": "⟨[⟦⦃(<⦃⦃{}⟦⟧⦄⦄>)⦄⟧]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟦⦃(<⦃⦃{",
"prompt_name": "reverse_perspective",
... |
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": 25,
"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": 13,
"full_sequence": "⟨<<⦃<{[<⦃⦃([⦃⦄<>⟨⟩])⟨⟩⦄{}⦄>]}>⦄>>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨<<⦃<{[<⦃⦃([⦃",
"prompt... |
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_variant": 3,
... |
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": 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 ... | {
"game_data": {
"answer": "⦃⟨⟨⟦⦃{{⟦⟨[[⟦{⟨⟦<⟦<<⟨⟩>>⟧>⟧⟩}⟧]]⟩⟧}}⦄⟧⟩⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "⦃⟨⟨⟦⦃{{⟦⟨[[⟦{⟨⟦<⟦<<⟨⟩>>⟧>⟧⟩}⟧]]⟩⟧}}⦄⟧⟩⟩⦄",
"n_types": 7,
"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": 21,
"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 backtic... | {
"game_data": {
"answer": "⟨⦅{⦃{⟨⦃⟦[⟨[(⟨⦅⦅<⦅⦃⦄⦅⦆⦆⟨⟩[]>⦃⦄⦆⟨⟩⦆⟩)]⟩]⟧⦄⟩}⦄}⦆⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "⟨⦅{⦃{⟨⦃⟦[⟨[(⟨⦅⦅<⦅⦃⦄⦅⦆⦆⟨⟩[]>⦃⦄⦆⟨⟩⦆⟩)]⟩]⟧⦄⟩}⦄}⦆⟩",
"n_types": 8,
"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": 3,
"nesting_depth": 0,
"opening_prefix": "(([[(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed"... |
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": 19,
"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... | {
"game_data": {
"answer": "⟨⟨{([[[⟦⦃<⟨⟨{}<><>⟩⟩()>⟨⟩⟦⟧⦄<>⟧]]])}⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"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": 18,
"full_sequence": "{[[(⟨<{⟨[[{<<[⟨((())⟨⟩)[]⟨⟩⟩]>>{}}]][]⟩}⟨⟩>⟨⟩⟩)<>][]]}()",
"n_types": 5,
"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 ext... | {
"game_data": {
"answer": "(({⦅⟦[<<[<{[[⟨⟦⦅⦃⟦⦃{⟦⟧}⦄⟧⦄⦆⟧⟩]]}>]>>]⟧⦆}))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"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 final an... | {
"game_data": {
"answer": "<<<(<[([{⟨⟨⟨[]⟩⟩()⟩}]<>)][]>)>>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "<<<(<[([{⟨⟨⟨[]⟩⟩()⟩}]<>)][]>)>>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<<(<[([{⟨⟨⟨[",
"prompt_nam... |
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": 1,
"full_sequence": "⟨<>⟩⟨⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 66789084,
... |
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": 2,
"full_sequence": "(<⟨⟩>⦃⦄)",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(<",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 62838... |
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": 4,
"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": 16,
"full_sequence": "<[⟨[([[[(<[⟦⟨<⟨<>⟩>[]⟨⟩⟩()⟧][]>()())[]]]⟦⟧<>]⟦⟧())]⟩[]<>()]>",
"n_types": 6,
"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": 16,
"full_sequence": "[[{[<([(<[[{[(<<>>)()]}[]<><>()()]{}()<>]><>)])>]}]<>]<>[]",
"n_types": 4,
"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 lik... | {
"game_data": {
"answer": "([{{{{([[([[(({{}{}}){})]])]])}}}}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "([{{{{([[([[(({{}{}}){})]])]])}}}}])",
"n_types": 3,
"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 ... | {
"game_data": {
"answer": "⟦(⦅[[{(⟦⟨⟨⟦⟦[⟨⟩]⦅⦆⦅⦆⟧⟦⟧⟧⟩⟩<>⟧⟨⟩)}]]⦆)⟧⦅⦆⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"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": 7,
"full_sequence": "([(({[()[]()]}()){}())[]])[]()[]",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(({[(",
"prompt_name": "te... |
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": 4,
"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 any extra bracket pairs ... | {
"game_data": {
"answer": "[(<([])>)]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[(<([])>)]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<([",
"prompt_name": "direct",
"prompt_variant": 0,
"seed"... |
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": 20,
"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": 24,
"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": 13,
"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 backtick... | {
"game_data": {
"answer": "⟨⦃⟨⟨⟦{{⟨<[<<([(⟨([{{[<[⦃[⟨[]⟩]⦄]>]}}])⟩)])>>]>⟩}}⟧⟩⟩⦄⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 26,
"full_sequence": "⟨⦃⟨⟨⟦{{⟨<[<<([(⟨([{{[<[⦃[⟨[]⟩]⦄]>]}}])⟩)])>>]>⟩}}⟧⟩⟩⦄⟩",
"n_types": 7,
"nesting_depth": 0,
"opening... |
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 ... | {
"game_data": {
"answer": "([{({(((({{{({[{}]})}}{}}))))})}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "([{({(((({{{({[{}]})}}{}}))))})}])",
"n_types": 3,
"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": 3,
"full_sequence": "((({})))[]()(){}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "technical",
"prompt_variant"... |
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 | 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 | 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": 7,
"full_sequence": "⦃[([[⟨[]⟩]])]⦄⟨⟩⟦⟧⟨⟩⟦⟧⟨⟩[]⟨⟩⟦⟧()",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃[([[⟨[",
"prompt_name": "di... |
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": 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": 20,
"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": 14,
"full_sequence": "[{<((<<{[{[[[[]]]]}]}>>))>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<((<<{[{[[[[",
"prompt_name": "fi... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[({",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 16... |
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": 19,
"full_sequence": "[({((([[<{{<<({<{([[][]()]<>)}>})>>}}>]])))})]",
"n_types": 4,
"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": 13,
"full_sequence": "⦅⦃⦅{⟨⟨[⟦{⟦⟦⦃<⦅⦆[]⦅⦆⟦⟧[]>⦄⟧⟧}⟧]⟩⟩}⦆⦄⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅⦃⦅{⟨⟨[⟦{⟦⟦⦃<",
"pr... |
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 pair... | {
"game_data": {
"answer": "((({}))){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "((({}))){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": ... |
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... | {
"game_data": {
"answer": "⦃[{⦃{⦃⦅<⟦⦃⦃⟨⟨⦃(⟦⦃[⦃<⟨[⦅⦆][]⟦⟧⟦⟧⟩{}⦃⦄>⦄]⦄⟧)⦄⟩⟩⦄⦄⟧>⦆⦄}⦄}]⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 23,
"full_sequence": "⦃[{⦃{⦃⦅<⟦⦃⦃⟨⟨⦃(⟦⦃[⦃<⟨[⦅⦆][]⟦⟧⟦⟧⟩{}⦃⦄>⦄]⦄⟧)⦄⟩⟩⦄⦄⟧>⦆⦄}⦄}]⦄",
"n_types": 8,
"nesting_depth": 0,
"ope... |
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": 6,
"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": 7,
"full_sequence": "⟨{⦃[⦃<()>⦃⦄⦄()]⦄<>}()[]<>⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⦃[⦃<(",
"prompt_name": "qa",
"pr... |
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 a... | {
"game_data": {
"answer": "{<⟨⟨({{{[{⟨⟨⟨⟨⟩⟨⟩⟩[]⟨⟩⟩⟩}]}}})⟩⟩>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "{<⟨⟨({{{[{⟨⟨⟨⟨⟩⟨⟩⟩[]⟨⟩⟩⟩}]}}})⟩⟩>}",
"n_types": 5,
"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 bra... | {
"game_data": {
"answer": "([{[{([[([{}[]]())]])}]}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "([{[{([[([{}[]]())]])}]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[{([[([",
"prompt_name": "direct",
... |
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": 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": 10,
"full_sequence": "([[[([({(()()[])}){}[]])[]]][]])()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[([({((",
"prompt_na... |
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": 25,
"full_sequence": "⟨⦃<((<{⟦⟦<⟨⟦{<[⟦⟦⟨⟦<⟨[{(⟨⟩)}]⟩>⟧[]⟩[]⟧⟧]>}⟧⟩>⟧⟧}>))>⦄⟩",
"n_types": 7,
"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": 17,
"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": 13,
"full_sequence": "[<<[(((<{([[[][]]]){}}<>>)))]>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<[(((<{([[[",
"prompt_nam... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 29... |
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": 5,
"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 `answ... | {
"game_data": {
"answer": "[{<[<[([{([])()}])]>]>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "[{<[<[([{([])()}])]>]>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<[<[([{(",
"prompt_name": "puzzle",
... |
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": 22,
"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": 3,
"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": 9,
"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 provi... | {
"game_data": {
"answer": "({({([{[()[]]}][]{}[][])}{})[]}{}){}{}{}()[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"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 `answer`. | {
"game_data": {
"answer": "{⦅⟨⟨⟦⟧⟩⦅⦆()⟩⦆}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "{⦅⟨⟨⟦⟧⟩⦅⦆()⟩⦆}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{⦅⟨⟨⟦",
"prompt_name": "story",
"prompt_variant": 4,
... |
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": 5,
"full_sequence": "{[{([()[]()])}[]]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[{([",
"prompt_name": "reverse_perspective",
"pro... |
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": 4,
"full_sequence": "(([[]])())",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 489... |
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": 4,
"nesting_depth": 0,
"opening_prefix": "[(<[[{",
"prompt_name": "qa",
"prompt_variant": 6,
"seed... |
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": 3,
"nesting_depth": 0,
"opening_prefix": "(({",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 12... |
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": 7,
"nesting_depth": 0,
"opening... |
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": 21,
"full_sequence": "[{{[([(<{(<<(<{[<{{<()>}[]}>]{}{}}<>>)<>>>)<>}[]>)])]}}]",
"n_types": 4,
"nesting_depth": 0,
"ope... |
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": 19,
"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": 17,
"full_sequence": "[<[([<{(([(({{([<>])}[]}[]{}))]))}>])]>]",
"n_types": 4,
"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": 11,
"full_sequence": "{{⟨<[{[({{<[]>}}())]}]>⟩}}",
"n_types": 5,
"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 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 | 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": 21,
"full_sequence": "<⟦⟦{⟦((([⟨[{(⟦<[⟦{[[<>⟨⟩]{}[]]}()⟧]>⟧())}]⟩])))⟧}⟧⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_pre... |
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": 6,
"nesting_depth": 0,
... |
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