env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x * y ** 1。
和 ◇，规则如下：
实数域上，x ◇ y = x - y - y ☆ x。
运算优先级：** > * = / = % = ◇ > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = abs(y - y * x) - y;
otherwise, x ▽ y = x / y + 1 + 5.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of t... | {
"game_data": {
"answer": "6.857143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = abs(y + x) + 3 - x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y + y + y.
The precedence of operations: ** > * = / = % = ◎ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 6 ◎ 2 ⊗ 2 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y - x + y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 △ 1
Please fill your final a... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + y * x + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x △ x + x - y).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * x - x ⊙ x.
The precedence of operations: △ = ⊗ > ** > * = / = % > + = - = ... | {
"game_data": {
"answer": "-11882",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 4 △ 7 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊕，规则如下：
当x小于y时，x ⊕ y = x * y * 3 + x；
其他情况下，x ⊕ y = y - x + y * y。
和 ▽，规则如下：
实数域上，x ▽ y = x + x ⊕ y * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + 4 ▽ x。
运算优先级：⊕ = ⊗ > ** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ▽ 2 ⊗ 8 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "606",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 2 ⊗ 8 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * 3 * x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y - x * x.
and ☆, the rules are as follows:
when y is a multiple of 5, x ☆ y = (x / y ◎ x);
otherwise, x ☆ y = abs(y * y + x).
The precedence of operations: ⊕ = ◎ >... | {
"game_data": {
"answer": "1784",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 1 ◎ 7 ☆ 1 * 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = (4 + x) * y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 7 + 7 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "424",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 7 + 7 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x - y * 4。
和 △，规则如下：
实数域上，x △ y = y - x ♢ x + 2。
和 ⊙，规则如下：
实数域上，x ⊙ y = 5 * 4 + y * x。
运算优先级：△ > ** > * = / = % = ♢ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♢ 8 △ 4 + 5 ⊙ 2 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1080",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 8 △ 4 + 5 ⊙ 2 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x - y + x.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 / 10 ▽ 3 % 1
Please fill your... | {
"game_data": {
"answer": "0.470588",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 10 ▽ 3 % 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ☆，规则如下：
当y是3的倍数时，x ☆ y = 2 / x * x - y；
其他情况下，x ☆ y = y + x - y。
和 ♢，规则如下：
当x是奇数时，x ♢ y = y ** (x ☆ x - y)；
其他情况下，x ♢ y = x * y ☆ x * y。
运算优先级：** > * = / = % > + = - = ☆ = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ☆ 2 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 2 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ▽, the rules are as follows:
when x is less than y, x ▽ y = y * x;
otherwise, x ▽ y = y * x * y.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 / 5 ... | {
"game_data": {
"answer": "23.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 5 ▽ 6 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = (x - 5 + y) / y。
和 ○，规则如下：
实数域上，x ○ y = x * abs(y + y) - x。
运算优先级：○ > ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♡ 2 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 2 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = y + y + x；
其他情况下，x △ y = y * (x) * x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ** 10 + 2 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 10 + 2 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♢, the rules are as follows:
when x is less than y, x ♢ y = x - y * x;
otherwise, x ♢ y = x + y.
and ▽, the rules are as follows:
when x is odd, x ▽ y = 3 - y - x ♢ 1;
otherwise, x ▽ y = x ♢ y + x * 5.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * y - y.
The precedence of opera... | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 2 ☆ 5 ▽ 1 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y + x。
和 ☆，规则如下：
当x等于y时，x ☆ y = x + x ◎ y；
其他情况下，x ☆ y = y + x ◎ 2。
运算优先级：◎ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 2 ☆ 10 * 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "47",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 2 ☆ 10 * 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
当x小于y时，x □ y = abs(y * x)；
其他情况下，x □ y = y + y - x。
和 ⊗，规则如下：
实数域上，x ⊗ y = 4 - y * x。
运算优先级：□ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 5 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-136",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 5 □ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = abs(x + x) * y。
和 △，规则如下：
当x和y的和是奇数时，x △ y = x * y - (y)；
其他情况下，x △ y = x + y + y。
运算优先级：♡ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 % 7 ♡ 8 ** 10 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 7 ♡ 8 ** 10 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x / 5 + y。
和 △，规则如下：
实数域上，x △ y = abs(y - x + 1 / y)。
和 ⊗，规则如下：
实数域上，x ⊗ y = y * x / y - y ⊕ y。
运算优先级：⊕ = ⊗ > ** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊗ 4 △ 9 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7.713636",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 4 △ 9 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * x - 2.
and ◇, the rules are as follows:
on the real number field, x ◇ y = abs(y + x).
The precedence of operations: ◇ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated... | {
"game_data": {
"answer": "5.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 5 ◎ 6 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ▽, the rules are as follows:
when x is greater than y, x ▽ y = y * y + x;
otherwise, x ▽ y = y - 5 + 1 * x.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the express... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = 5 * x + y.
and ▽, the rules are as follows:
when y is even, x ▽ y = x * (x * y);
otherwise, x ▽ y = x + y / x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (y * x).
The precedence of operations: ** = ▽ > * = / = % = ♡ > ... | {
"game_data": {
"answer": "154.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 8 ▽ 1 ⊕ 8 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
当y是奇数时，x ⊗ y = y + x；
其他情况下，x ⊗ y = y + x ** 2 - y - (x)。
和 ♡，规则如下：
当x等于y时，x ♡ y = 3 + abs(x - 1) * y；
其他情况下，x ♡ y = 1 + y - 4 + x。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = x / y + x - y + x；
其他情况下，x ☆ y = x / x - (y + x) + y。
运算优先级：⊗ > ** = ♡ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♡ 8 ☆ ... | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 8 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + abs(x + y).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 10
Please fill your fi... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y / y * x * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x ** y + y) + y - y.
The precedence of operations: ** > * = / = % > + = - = ◎ = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses... | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = y - 4 + x + 1；
其他情况下，x ♡ y = x * y + x - x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x ♡ x + y - y。
运算优先级：⊕ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + x + y + y + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y ☆ (x / y).
The precedence of operations: ** > * = / = % = ☆ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is c... | {
"game_data": {
"answer": "71.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 6 ☆ 9 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = (4 - x / y).
and □, the rules are as follows:
when x is odd, x □ y = y - y - x;
otherwise, x □ y = x * y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / y.
The precedence of operations: ⊙ = □ > ♢ > ** > * = / = % > + =... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 9 ⊙ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y * x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ☆ y - x.
The precedence of operations: ☆ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated firs... | {
"game_data": {
"answer": "73",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 + 1 ☆ 9 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - y / x / x - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 4 * abs(y) * x - y.
and □, the rules are as follows:
on the real number field, x □ y = y + x + x.
The precedence of operations: ♢ > ** = ☆ > * = / = % > + = -... | {
"game_data": {
"answer": "179",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 6 □ 1 ☆ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y + x - y - x + x。
和 ♢，规则如下：
实数域上，x ♢ y = x ♡ y * x。
运算优先级：♡ = ♢ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 - 4 % 4 ♢ 4 ♡ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 4 % 4 ♢ 4 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x - y / 5 - abs(x)。
和 ♡，规则如下：
实数域上，x ♡ y = y - x - 4 + x * y。
和 ○，规则如下：
实数域上，x ○ y = y * y - x + x * x。
运算优先级：⊗ > ○ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊗ 1 / 5 ○ 8 ** 3 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.999997",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 1 / 5 ○ 8 ** 3 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + (y + x)。
和 △，规则如下：
实数域上，x △ y = x ♡ y + y。
运算优先级：** = △ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 3 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 3 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
when x and y are both odd, x ◎ y = x - y - x - y;
otherwise, x ◎ y = y * y - x + y.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = x * y ◎ y - y;
otherwise, x □ y = 3 + y ◎ x * y.
The precedence of operations: □ > ** = ◎ > * = / = % > + = -。
Parentheses h... | {
"game_data": {
"answer": "-44374",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 8 □ 1 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ♡，规则如下：
当x小于y时，x ♡ y = 1 - y + y * y * x；
其他情况下，x ♡ y = (4 + x + y / y)。
和 ♢，规则如下：
实数域上，x ♢ y = (y + x / y)。
运算优先级：** = ♡ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ** 5 ♡ 10 ♢ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 5 ♡ 10 ♢ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - y - x。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y / y - x * y * x；
其他情况下，x ◎ y = x - x - y + y * x。
运算优先级：□ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y / x * 3.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + 2 + x.
and △, the rules are as follows:
on the real number field, x △ y = x + (y + x).
The precedence of operations: ◇ > ** = ⊙ > * = / = % = △ > + = -。
Parenthes... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 7 ◇ 7 ⊙ 8 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = (x) * y；
其他情况下，x ☆ y = x ** y / x。
和 ♡，规则如下：
当x等于y时，x ♡ y = y ☆ x；
其他情况下，x ♡ y = y / x + y。
运算优先级：☆ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♡ 7 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 7 ☆ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y - x + y + 2.
and ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y = x * 4 / y ⊙ 3;
otherwise, x ⊗ y = x ⊙ y * y * x.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = y ⊙ x / y - x / y;
otherwise, x □ y = ... | {
"game_data": {
"answer": "3744",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 + 1 ⊗ 10 □ 8 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ○，规则如下：
当y是奇数时，x ○ y = y ** x * x；
其他情况下，x ○ y = 4 / x * y + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = 5 / x - 4 + x - y。
和 ♡，规则如下：
实数域上，x ♡ y = x □ y + y * x - x。
运算优先级：** > * = / = % > + = - = □ = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 □ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | 定义 ⊙，规则如下：
当y是奇数时，x ⊙ y = x - x * x - y；
其他情况下，x ⊙ y = x - x - y - 3。
和 ⊗，规则如下：
实数域上，x ⊗ y = x + y * x * 2。
和 □，规则如下：
当x和y都是奇数时，x □ y = x * y - 2 - y；
其他情况下，x □ y = x - x / y - y。
运算优先级：** = ⊗ = □ > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 / 5 ⊗ 5 □ 7 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 5 ⊗ 5 □ 7 ⊙ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x + y * y。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y * x；
其他情况下，x ☆ y = x + y / 3。
和 ⊙，规则如下：
实数域上，x ⊙ y = x - y * 2。
运算优先级：♢ > ⊙ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 3 ⊙ 5 ♢ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-68",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 3 ⊙ 5 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
when x is a multiple of 3, x ♡ y = x - x + y / x;
otherwise, x ♡ y = x - abs(y + y) * y.
and ○, the rules are as follows:
on the real number field, x ○ y = 2 + 5 + y + x.
The precedence of operations: ♡ > ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and th... | {
"game_data": {
"answer": "-8.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 % 10 - 9 ♡ 5 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
当x是3的倍数时，x ○ y = abs(y - y) - x；
其他情况下，x ○ y = 2 - x ** y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ○ 8 / 6 % 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8.902724",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 8 / 6 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = abs(y + x) - x + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y / x) * 3 ☆ y - x.
The precedence of operations: ** > * = / = % = ☆ = ⊗ > + = -。
Parentheses have the highest priority, and the expression inside the parenth... | {
"game_data": {
"answer": "-4.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y + x。
和 ○，规则如下：
当y是奇数时，x ○ y = x - x ⊙ y；
其他情况下，x ○ y = abs(y * x)。
和 ♢，规则如下：
当x是3的倍数时，x ♢ y = x + y + y；
其他情况下，x ♢ y = x ○ y - x。
运算优先级：⊙ > ♢ > ** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♢ 10 ○ 2 ⊙ 9 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 10 ○ 2 ⊙ 9 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = abs(y * 3 ** 2) - x * x。
和 ▽，规则如下：
实数域上，x ▽ y = x / y ◎ x - x * x。
运算优先级：▽ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 + 10 ▽ 7 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.671803",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 + 10 ▽ 7 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y * x * y + x。
和 ◇，规则如下：
实数域上，x ◇ y = y - x - x - x。
运算优先级：** > * = / = % = ▽ = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "500",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | 定义 ○，规则如下：
当y是奇数时，x ○ y = y * x * 5；
其他情况下，x ○ y = y + x * y + y * x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = (5 + 2 - y - x * y).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ▽ 4
Please fill you... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ◇，规则如下：
当x和y的和是奇数时，x ◇ y = y + x + y；
其他情况下，x ◇ y = y ** (y) - y - x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 - 3 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 3 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = x - y + y;
otherwise, x ⊕ y = x + 1 + y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (y ⊕ y) - y + x.
and ▽, the rules are as follows:
when x is equal to y, x ▽ y = x + y + y ♡ x;
otherwise, x ▽ y = 5 + x / y * x.
The precedence... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 9 ♡ 9 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
当x大于y时，x ○ y = x * y - x；
其他情况下，x ○ y = y / x + x。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.428571",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
当x是偶数时，x □ y = x - x * y + x * 5；
其他情况下，x □ y = x / y + y。
和 ☆，规则如下：
实数域上，x ☆ y = y + x。
运算优先级：** > * = / = % > + = - = □ = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 9 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 9 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y * y / 2 + x。
和 ○，规则如下：
当x大于y时，x ○ y = y * y * y * x；
其他情况下，x ○ y = x + y + y / y。
运算优先级：** > * = / = % = □ = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 □ 6 ○ 1 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 6 ○ 1 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y + x。
和 ◎，规则如下：
实数域上，x ◎ y = x / y - x。
运算优先级：◎ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◎ 6 * 5 ♡ 1
请将最终答案填入\boxed{}中。 | {
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"difficulty": 1,
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"expression": "4 ◎ 6 * 5 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
when x is even, x ⊕ y = x - (y) + y + 1;
otherwise, x ⊕ y = x + y * x + x ** y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 3 - x - y + 4.
and ♡, the rules are as follows:
on the real number field, x ♡ y = 1 * x ⊕ x + y.
The precedence of operations: ♡ ... | {
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"answer": "-47",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 7 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = 1 / x - y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y + x ♢ y.
and △, the rules are as follows:
on the real number field, x △ y = y - (x) + y + y ⊗ x.
The precedence of operations: ♢ > ⊗ > ** > * = / = % = △ > + = ... | {
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"answer": "3.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "7 △ 3 ⊗ 4",
"fill_length": null,
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x / y * 3。
和 ⊕，规则如下：
当x和y的和是奇数时，x ⊕ y = y / x - y；
其他情况下，x ⊕ y = y * 4 * x。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = y △ x；
其他情况下，x ♡ y = x + 1 + y。
运算优先级：** = △ = ⊕ = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊕ 1 ♡ 10 △ 1 - 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "109",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 1 ♡ 10 △ 1 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = abs(x + y) - y.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = (y △ x);
otherwise, x ◎ y = (x + y + 3 △ y) * 4.
The precedence of operations: ** = △ > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the ex... | {
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"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y * x * y - x。
和 ○，规则如下：
实数域上，x ○ y = y * y - x / y。
运算优先级：** = □ = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 % 7 □ 6 ○ 1 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 7 □ 6 ○ 1 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = x - x ** x + y;
otherwise, x ▽ y = x - y ** y - x.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value o... | {
"game_data": {
"answer": "-27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 6 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = x - y * 2;
otherwise, x △ y = x * (2 * y).
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 + 9 △... | {
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"answer": "224",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 + 9 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y * x - 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x ▽ 4。
和 ☆，规则如下：
实数域上，x ☆ y = y - y - abs(x)。
运算优先级：⊗ > ** = ▽ = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 2 ▽ 5 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-191",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 2 ▽ 5 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * abs(4 / y - x)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 - 5 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 5 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◎，规则如下：
当x是偶数时，x ◎ y = 5 + 4 * x - y / x；
其他情况下，x ◎ y = y + x。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y * y + y - y * x；
其他情况下，x ☆ y = x * x - (y ◎ y ** 4)。
运算优先级：☆ > ** = ◎ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / y - y.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 / 9 △ 10
Please fill your fin... | {
"game_data": {
"answer": "-9.955556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 9 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y * x * x * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ◇ 4 / 10 ◇ 4
Please fill... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 4 / 10 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = (x * y) / 2；
其他情况下，x ☆ y = abs(x) ** x * y。
和 ◎，规则如下：
当y是奇数时，x ◎ y = y + x + y；
其他情况下，x ◎ y = x ☆ x - y + x。
运算优先级：** > * = / = % > + = - = ☆ = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 1 % 7 ☆ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 1 % 7 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = x * abs(2 / y - 1 + y);
otherwise, x ♡ y = y + x / 1.
and □, the rules are as follows:
on the real number field, x □ y = x - x ♡ x + y + (x).
The precedence of operations: ** = □ > * = / = % = ♡ > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 8 □ 4 + 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ▽，规则如下：
当y是5的倍数时，x ▽ y = 1 + y - x / y；
其他情况下，x ▽ y = x + y * y - x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = 5 - y - x;
otherwise, x ⊙ y = (y / x).
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x - x + y;
otherwise, x ⊗ y = x + y.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = abs(y + y - x);
othe... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 6 ⊗ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊙，规则如下：
当y是奇数时，x ⊙ y = (x * y - x * 5)；
其他情况下，x ⊙ y = y * y - x - 3。
和 ⊕，规则如下：
实数域上，x ⊕ y = x + y ** 1 ⊙ 3 - y。
和 ◎，规则如下：
实数域上，x ◎ y = x * y + (x ⊕ 2) - 4。
运算优先级：⊙ = ⊕ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊙ 7 % 6 ◎ 9 ⊕ 9 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-15.669753",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 7 % 6 ◎ 9 ⊕ 9 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y ** x。
和 ◎，规则如下：
实数域上，x ◎ y = y * abs(x + x)。
运算优先级：** = □ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 2 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "648",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 2 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + x * x + y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 % 10 ** 9 △ 5
Please fill... | {
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"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 10 ** 9 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
当x等于y时，x ◎ y = y + x / y - x；
其他情况下，x ◎ y = x + y * y。
和 ◇，规则如下：
实数域上，x ◇ y = y * y - y ◎ x。
运算优先级：◎ > ** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 6 ◇ 4 + 7 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1882",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 6 ◇ 4 + 7 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ⊕，规则如下：
当x和y的和是奇数时，x ⊕ y = y - y ** x；
其他情况下，x ⊕ y = 3 / 3 + y ** x。
和 ◇，规则如下：
实数域上，x ◇ y = x + y - x ⊕ x。
和 ⊙，规则如下：
当x小于y时，x ⊙ y = y * (x + 4) + y；
其他情况下，x ⊙ y = y * y - x * y。
运算优先级：◇ = ⊙ > ** > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊙ 10 ◇ 8 ⊕ 10 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 10 ◇ 8 ⊕ 10 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + y * x + y * 4。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 - 8 ○ 3 / 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 8 ○ 3 / 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - y - y * x - y.
and ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = x + x * y - x;
otherwise, x ⊕ y = x ♢ x / x * x ** (y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x / y.
The precedence of ope... | {
"game_data": {
"answer": "1.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 10 / 10 ⊕ 9 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y + x + x / y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ○ 2
Please fill your fina... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x + 5 + 3 * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ▽ 5 * 7 - 2
Please fill y... | {
"game_data": {
"answer": "201",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 5 * 7 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = abs(y * x - x) + y。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = y + x * y + 1；
其他情况下，x ◎ y = x ♡ y。
运算优先级：** = ♡ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "100",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is even, x △ y = (y / x) - x;
otherwise, x △ y = abs(x + y).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"game_data": {
"answer": "1.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 / 4 △ 6 ** 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = abs(y * y + x) + 4;
otherwise, x ○ y = x - y + x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 6 + 5 - 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 1 + y - y / x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 - 6 ▽ 2 + 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 6 ▽ 2 + 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 △，规则如下：
当x等于y时，x △ y = abs(y * x) - 1 ** y；
其他情况下，x △ y = y + y + y - x。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 △ 6 + 1 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 6 + 1 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define △, the rules are as follows:
when x is equal to y, x △ y = x + y;
otherwise, x △ y = x * (x + y).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 8... | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 8 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x是5的倍数时，x ▽ y = x - x + y - y - y；
其他情况下，x ▽ y = x * y + y + x * x。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "161",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x + y - x。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + x + x - y。
和 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = (y - x + y - y) * y；
其他情况下，x ⊗ y = (x □ y - x + x) - y。
运算优先级：□ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = y - x - x。
和 ⊗，规则如下：
实数域上，x ⊗ y = (x * y) ♢ y。
和 ☆，规则如下：
当x和y都是奇数时，x ☆ y = x * y * y；
其他情况下，x ☆ y = (y) + x + x。
运算优先级：♢ > ** = ☆ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ♢ 7 ☆ 5 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 7 ☆ 5 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = abs(y) + x.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 - 2 ** 8 ▽ 4
Please fill you... | {
"game_data": {
"answer": "-255",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 2 ** 8 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x / y + x；
其他情况下，x ▽ y = x * y + y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ▽ 2 * 8 % 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 2 * 8 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y - x / x。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◇，规则如下：
当x大于y时，x ◇ y = y / 2 / 2 - y * x；
其他情况下，x ◇ y = y + y * abs(y + 1 / x)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◇ 9 * 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-87.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 9 * 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = 3 + x / y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 6
Please fill your final an... | {
"game_data": {
"answer": "3.833333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = x * 4 / y；
其他情况下，x ⊙ y = x ** y * 3。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = x ⊙ y + y；
其他情况下，x ♡ y = y + x / y。
和 ▽，规则如下：
实数域上，x ▽ y = y * x。
运算优先级：⊙ > ** > * = / = % = ♡ = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊙ 5 ▽ 2 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 5 ▽ 2 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y / y * x + x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y - (y) - y - x。
和 ☆，规则如下：
实数域上，x ☆ y = 1 * y ⊕ x * 2。
运算优先级：⊕ = ☆ > ⊗ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ⊗ 3 ⊕ 3 + 6 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 3 ⊕ 3 + 6 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ♡, the rules are as follows:
when y is even, x ♡ y = y + x + y / x;
otherwise, x ♡ y = x + y * (y) + y.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x / y * y / y - x;
otherwise, x ○ y = x * y - y * abs(y * 4).
The precedence of operations: ♡ = ○ > ** > * = / = % > + = -。
Parenthes... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 5 + 3 ○ 7 % 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
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