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In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (3, 4, 4). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:
1. (x', y, z) such that x AND x' = x
2. (x, y', z) such that y AND y' = y
3. (x, ... | {"environment": "BannedPointSupersetPathCounting", "config": {"seed": 40, "parameter": {"MAX_N_M_R": 6, "MAX_O": 20, "N": 3, "M": 4, "R": 4, "O": 1, "obstacles": [[0, 4, 0]], "MOD": 5710, "reference_answer": 22}, "passing_reward_threshold": 1.0}} |
In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (3, 2, 1). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:
1. (x', y, z) such that x AND x' = x
2. (x, y', z) such that y AND y' = y
3. (x, ... | {"environment": "BannedPointSupersetPathCounting", "config": {"seed": 41, "parameter": {"MAX_N_M_R": 6, "MAX_O": 20, "N": 3, "M": 2, "R": 1, "O": 3, "obstacles": [[2, 2, 0], [0, 0, 1], [0, 2, 1]], "MOD": 7089, "reference_answer": 15}, "passing_reward_threshold": 1.0}} |
In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (5, 0, 0). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:
1. (x', y, z) such that x AND x' = x
2. (x, y', z) such that y AND y' = y
3. (x, ... | {"environment": "BannedPointSupersetPathCounting", "config": {"seed": 42, "parameter": {"MAX_N_M_R": 6, "MAX_O": 20, "N": 5, "M": 0, "R": 0, "O": 2, "obstacles": [[4, 0, 0], [1, 0, 0]], "MOD": 5883, "reference_answer": 1}, "passing_reward_threshold": 1.0}} |
In a three-dimensional space, you start at point (0, 0, 0) and want to reach the point (0, 2, 5). At each step, if you are currently at (x, y, z), you may move to a new (different from the current one) point of one of the following types:
1. (x', y, z) such that x AND x' = x
2. (x, y', z) such that y AND y' = y
3. (x, ... | {"environment": "BannedPointSupersetPathCounting", "config": {"seed": 43, "parameter": {"MAX_N_M_R": 6, "MAX_O": 20, "N": 0, "M": 2, "R": 5, "O": 2, "obstacles": [[0, 2, 4], [0, 2, 0]], "MOD": 8397, "reference_answer": 4}, "passing_reward_threshold": 1.0}} |
Given an array A of length 8:
8 1 4 5 4 3 6 5
Repeat array A 7 times to form a new array B of length 8 * 7 = 56. In the new array B, how many (nonempty) contiguous subarrays have a total sum less than or equal to 233?
**Output Format:** Your final answer should be a single integer — the total number of (nonempty) sub... | {"environment": "BoundedSubarrayCounting", "config": {"seed": 40, "parameter": {"N": 8, "M": 7, "A": [8, 1, 4, 5, 4, 3, 6, 5], "K": 233, "reference_answer": 1584}, "passing_reward_threshold": 1.0}} |
Given an array A of length 8:
7 6 4 3 7 5 5 7
Repeat array A 7 times to form a new array B of length 8 * 7 = 56. In the new array B, how many (nonempty) contiguous subarrays have a total sum less than or equal to 302?
**Output Format:** Your final answer should be a single integer — the total number of (nonempty) sub... | {"environment": "BoundedSubarrayCounting", "config": {"seed": 41, "parameter": {"N": 8, "M": 7, "A": [7, 6, 4, 3, 7, 5, 5, 7], "K": 302, "reference_answer": 1595}, "passing_reward_threshold": 1.0}} |
Given an array A of length 8:
2 1 5 4 4 3 2 2
Repeat array A 7 times to form a new array B of length 8 * 7 = 56. In the new array B, how many (nonempty) contiguous subarrays have a total sum less than or equal to 156?
**Output Format:** Your final answer should be a single integer — the total number of (nonempty) sub... | {"environment": "BoundedSubarrayCounting", "config": {"seed": 42, "parameter": {"N": 8, "M": 7, "A": [2, 1, 5, 4, 4, 3, 2, 2], "K": 156, "reference_answer": 1590}, "passing_reward_threshold": 1.0}} |
Given an array A of length 8:
1 5 3 8 6 2 8 8
Repeat array A 7 times to form a new array B of length 8 * 7 = 56. In the new array B, how many (nonempty) contiguous subarrays have a total sum less than or equal to 17?
**Output Format:** Your final answer should be a single integer — the total number of (nonempty) suba... | {"environment": "BoundedSubarrayCounting", "config": {"seed": 43, "parameter": {"N": 8, "M": 7, "A": [1, 5, 3, 8, 6, 2, 8, 8], "K": 17, "reference_answer": 171}, "passing_reward_threshold": 1.0}} |
You are given 10 coins in a row (1-indexed from left to right). The i-th coin has value C[i]: C[1]=15 C[2]=19 C[3]=17 C[4]=2 C[5]=8 C[6]=10 C[7]=7 C[8]=5 C[9]=12 C[10]=9
Alice and Bob play alternately, with Alice going first. On a turn, a player removes some **positive number** of **leftmost** coins and adds the sum of... | {"environment": "CoinSquareGame", "config": {"seed": 40, "parameter": {"N": 10, "C": [15, 19, 17, 2, 8, 10, 7, 5, 12, 9], "reference_answer": 63}, "passing_reward_threshold": 1.0}} |
You are given 10 coins in a row (1-indexed from left to right). The i-th coin has value C[i]: C[1]=13 C[2]=11 C[3]=8 C[4]=6 C[5]=13 C[6]=19 C[7]=10 C[8]=18 C[9]=9 C[10]=13
Alice and Bob play alternately, with Alice going first. On a turn, a player removes some **positive number** of **leftmost** coins and adds the sum ... | {"environment": "CoinSquareGame", "config": {"seed": 41, "parameter": {"N": 10, "C": [13, 11, 8, 6, 13, 19, 10, 18, 9, 13], "reference_answer": 71}, "passing_reward_threshold": 1.0}} |
You are given 10 coins in a row (1-indexed from left to right). The i-th coin has value C[i]: C[1]=4 C[2]=1 C[3]=9 C[4]=8 C[5]=8 C[6]=5 C[7]=4 C[8]=18 C[9]=3 C[10]=19
Alice and Bob play alternately, with Alice going first. On a turn, a player removes some **positive number** of **leftmost** coins and adds the sum of th... | {"environment": "CoinSquareGame", "config": {"seed": 42, "parameter": {"N": 10, "C": [4, 1, 9, 8, 8, 5, 4, 18, 3, 19], "reference_answer": 40}, "passing_reward_threshold": 1.0}} |
You are given 10 coins in a row (1-indexed from left to right). The i-th coin has value C[i]: C[1]=2 C[2]=10 C[3]=5 C[4]=15 C[5]=12 C[6]=4 C[7]=15 C[8]=20 C[9]=16 C[10]=20
Alice and Bob play alternately, with Alice going first. On a turn, a player removes some **positive number** of **leftmost** coins and adds the sum ... | {"environment": "CoinSquareGame", "config": {"seed": 43, "parameter": {"N": 10, "C": [2, 10, 5, 15, 12, 4, 15, 20, 16, 20], "reference_answer": 63}, "passing_reward_threshold": 1.0}} |
You are given a set of 10 points on a 2D plane labeled from 0 to 9.
It is guaranteed that:
(1) all the coordinates are integers;
(2) no two points have the same coordinates;
(3) no three points are on the same line.
Below is the set of points:
(3, 4)
(2, 0)
(8, 0)
(7, 9)
(10, 10)
(10, 3)
(0, 8)
(2, 5)
(9, 7)
(4, 7)
Yo... | {"environment": "ConvexHull", "config": {"seed": 40, "parameter": {"N": 10, "points": [[3, 4], [2, 0], [8, 0], [7, 9], [10, 10], [10, 3], [0, 8], [2, 5], [9, 7], [4, 7]], "reference_answer": 158}, "passing_reward_threshold": 1.0}} |
You are given a set of 10 points on a 2D plane labeled from 0 to 9.
It is guaranteed that:
(1) all the coordinates are integers;
(2) no two points have the same coordinates;
(3) no three points are on the same line.
Below is the set of points:
(0, 1)
(0, 7)
(9, 0)
(6, 5)
(9, 9)
(4, 6)
(4, 8)
(2, 2)
(3, 2)
(6, 9)
Your ... | {"environment": "ConvexHull", "config": {"seed": 41, "parameter": {"N": 10, "points": [[0, 1], [0, 7], [9, 0], [6, 5], [9, 9], [4, 6], [4, 8], [2, 2], [3, 2], [6, 9]], "reference_answer": 141}, "passing_reward_threshold": 1.0}} |
You are given a set of 10 points on a 2D plane labeled from 0 to 9.
It is guaranteed that:
(1) all the coordinates are integers;
(2) no two points have the same coordinates;
(3) no three points are on the same line.
Below is the set of points:
(0, 4)
(2, 1)
(10, 8)
(10, 1)
(3, 10)
(3, 3)
(8, 9)
(6, 0)
(0, 8)
(1, 9)
Yo... | {"environment": "ConvexHull", "config": {"seed": 42, "parameter": {"N": 10, "points": [[0, 4], [2, 1], [10, 8], [10, 1], [3, 10], [3, 3], [8, 9], [6, 0], [0, 8], [1, 9]], "reference_answer": 166}, "passing_reward_threshold": 1.0}} |
You are given a set of 10 points on a 2D plane labeled from 0 to 9.
It is guaranteed that:
(1) all the coordinates are integers;
(2) no two points have the same coordinates;
(3) no three points are on the same line.
Below is the set of points:
(9, 0)
(0, 4)
(2, 7)
(1, 1)
(2, 0)
(9, 5)
(5, 10)
(1, 7)
(8, 6)
(6, 6)
Your... | {"environment": "ConvexHull", "config": {"seed": 43, "parameter": {"N": 10, "points": [[9, 0], [0, 4], [2, 7], [1, 1], [2, 0], [9, 5], [5, 10], [1, 7], [8, 6], [6, 6]], "reference_answer": 133}, "passing_reward_threshold": 1.0}} |
Now consider a number system with base 8, which uses digits d[0], d[1], ..., d[7].
Each d[i] is a unique integer in the range [0, 7], but their actual values are unknown.
We define the number `d[i0]d[i1]...d[ik]` to represent the value `d[i0] * 8^k + d[i1] * 8^(k-1) + ... + d[ik] * 8^0`,
where `d[i]` is the actual dig... | {"environment": "Cryptarithmetic", "config": {"seed": 40, "parameter": {"N": 8, "addend_length": 11, "digits": [2, 5, 3, 1, 0, 6, 4, 7], "reference_answer": "2 5 3 1 0 6 4 7", "addend_1": [2, 5, 4, 7, 0, 2, 0, 3, 7, 0, 2], "addend_2": [5, 1, 4, 5, 2, 1, 6, 0, 5, 5, 2], "sum_result": [7, 6, 0, 5, 3, 3, 6, 3, 4, 6, 4]}, ... |
Now consider a number system with base 8, which uses digits d[0], d[1], ..., d[7].
Each d[i] is a unique integer in the range [0, 7], but their actual values are unknown.
We define the number `d[i0]d[i1]...d[ik]` to represent the value `d[i0] * 8^k + d[i1] * 8^(k-1) + ... + d[ik] * 8^0`,
where `d[i]` is the actual dig... | {"environment": "Cryptarithmetic", "config": {"seed": 41, "parameter": {"N": 8, "addend_length": 12, "digits": [0, 4, 7, 3, 5, 1, 2, 6], "reference_answer": "0 4 7 3 5 1 2 6", "addend_1": [4, 6, 0, 3, 0, 7, 2, 2, 5, 2, 4, 6], "addend_2": [0, 1, 0, 6, 4, 3, 1, 5, 7, 2, 0, 1], "sum_result": [4, 7, 0, 1, 5, 2, 4, 7, 4, 5,... |
Now consider a number system with base 8, which uses digits d[0], d[1], ..., d[7].
Each d[i] is a unique integer in the range [0, 7], but their actual values are unknown.
We define the number `d[i0]d[i1]...d[ik]` to represent the value `d[i0] * 8^k + d[i1] * 8^(k-1) + ... + d[ik] * 8^0`,
where `d[i]` is the actual dig... | {"environment": "Cryptarithmetic", "config": {"seed": 42, "parameter": {"N": 8, "addend_length": 13, "digits": [3, 4, 6, 7, 2, 5, 0, 1], "reference_answer": "3 4 6 7 2 5 0 1", "addend_1": [1, 1, 6, 0, 0, 1, 3, 3, 0, 3, 6, 3, 4], "addend_2": [4, 0, 2, 6, 5, 4, 2, 3, 5, 1, 1, 6, 1], "sum_result": [5, 1, 0, 7, 5, 5, 5, 6,... |
Now consider a number system with base 8, which uses digits d[0], d[1], ..., d[7].
Each d[i] is a unique integer in the range [0, 7], but their actual values are unknown.
We define the number `d[i0]d[i1]...d[ik]` to represent the value `d[i0] * 8^k + d[i1] * 8^(k-1) + ... + d[ik] * 8^0`,
where `d[i]` is the actual dig... | {"environment": "Cryptarithmetic", "config": {"seed": 43, "parameter": {"N": 8, "addend_length": 14, "digits": [6, 7, 4, 3, 1, 5, 2, 0], "reference_answer": "6 7 4 3 1 5 2 0", "addend_1": [7, 7, 0, 6, 5, 6, 6, 2, 0, 1, 1, 6, 2, 1], "addend_2": [2, 7, 2, 6, 4, 2, 6, 1, 0, 0, 2, 0, 2, 3], "sum_result": [1, 7, 3, 4, 2, 1,... |
You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(7, 8)
(2, 7)
(2, 3)
(3, 6)
(3, 8)
(1, 5)
(1, 2)
(2, 5)
(0, 1)
Please count the number of simple cycles in the graph. A simple cycle is a cycle with at least 3 vertices, with no repeated v... | {"environment": "CycleCounting", "config": {"seed": 1040, "parameter": {"N": 9, "edge_density": 0.25, "edges": [[7, 8], [2, 7], [2, 3], [3, 6], [3, 8], [1, 5], [1, 2], [2, 5], [0, 1]], "reference_answer": 2}, "passing_reward_threshold": 1.0}} |
You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(5, 8)
(4, 7)
(4, 8)
(0, 7)
(7, 8)
(4, 6)
(1, 6)
(4, 5)
(5, 6)
(3, 6)
(2, 8)
(1, 4)
(3, 7)
(2, 4)
(0, 3)
(0, 1)
Please count the number of simple cycles in the graph. A simple cycle is a c... | {"environment": "CycleCounting", "config": {"seed": 1041, "parameter": {"N": 9, "edge_density": 0.45, "edges": [[5, 8], [4, 7], [4, 8], [0, 7], [7, 8], [4, 6], [1, 6], [4, 5], [5, 6], [3, 6], [2, 8], [1, 4], [3, 7], [2, 4], [0, 3], [0, 1]], "reference_answer": 85}, "passing_reward_threshold": 1.0}} |
You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(4, 8)
(0, 1)
(3, 8)
(0, 2)
(5, 6)
(3, 7)
(3, 4)
(1, 2)
(1, 7)
(4, 7)
(2, 3)
(3, 5)
(1, 3)
(7, 8)
(0, 4)
(2, 4)
(6, 8)
(5, 7)
(1, 4)
(6, 7)
(3, 6)
(1, 6)
(0, 6)
Please count the number of ... | {"environment": "CycleCounting", "config": {"seed": 1042, "parameter": {"N": 9, "edge_density": 0.65, "edges": [[4, 8], [0, 1], [3, 8], [0, 2], [5, 6], [3, 7], [3, 4], [1, 2], [1, 7], [4, 7], [2, 3], [3, 5], [1, 3], [7, 8], [0, 4], [2, 4], [6, 8], [5, 7], [1, 4], [6, 7], [3, 6], [1, 6], [0, 6]], "reference_answer": 126... |
You are given an **undirected graph** with 9 vertices, labeled from `0` to `8`. The graph contains the following undirected edges:
(0, 1)
(1, 4)
(1, 7)
(4, 5)
(5, 7)
(3, 6)
(0, 3)
(4, 7)
(2, 5)
(2, 7)
(0, 6)
(1, 8)
(3, 5)
(1, 2)
(0, 8)
(0, 5)
(1, 3)
(3, 4)
(2, 3)
(0, 4)
(6, 7)
(0, 2)
(2, 6)
(6, 8)
(7, 8)
(5, 8)
(4, 6)
... | {"environment": "CycleCounting", "config": {"seed": 1043, "parameter": {"N": 9, "edge_density": 0.85, "edges": [[0, 1], [1, 4], [1, 7], [4, 5], [5, 7], [3, 6], [0, 3], [4, 7], [2, 5], [2, 7], [0, 6], [1, 8], [3, 5], [1, 2], [0, 8], [0, 5], [1, 3], [3, 4], [2, 3], [0, 4], [6, 7], [0, 2], [2, 6], [6, 8], [7, 8], [5, 8], ... |
A **double cross** is a specific shape consisting of two horizontal and one vertical segments of `1`s. For example:
```
..........
....1..... ..1..
..11111... .111.
....1..... ..1..
.1111111.. 11111
....1..... ..1..
....1.....
..........
```
A valid double cross must satisfy the following condi... | {"environment": "DoubleCrossCounting", "config": {"seed": 40, "parameter": {"MAX_N_M": 10, "N": 8, "M": 9, "zero_coordinates": [[0, 4], [3, 4], [4, 0], [2, 8], [1, 7], [4, 8], [3, 8], [6, 2], [0, 3], [3, 6], [6, 3], [5, 2], [0, 8], [7, 0], [4, 5], [1, 3], [4, 3]], "reference_answer": 0}, "passing_reward_threshold": 1.0... |
A **double cross** is a specific shape consisting of two horizontal and one vertical segments of `1`s. For example:
```
..........
....1..... ..1..
..11111... .111.
....1..... ..1..
.1111111.. 11111
....1..... ..1..
....1.....
..........
```
A valid double cross must satisfy the following condi... | {"environment": "DoubleCrossCounting", "config": {"seed": 41, "parameter": {"MAX_N_M": 10, "N": 8, "M": 7, "zero_coordinates": [[1, 3], [3, 3], [5, 1], [6, 2]], "reference_answer": 12}, "passing_reward_threshold": 1.0}} |
A **double cross** is a specific shape consisting of two horizontal and one vertical segments of `1`s. For example:
```
..........
....1..... ..1..
..11111... .111.
....1..... ..1..
.1111111.. 11111
....1..... ..1..
....1.....
..........
```
A valid double cross must satisfy the following condi... | {"environment": "DoubleCrossCounting", "config": {"seed": 42, "parameter": {"MAX_N_M": 10, "N": 10, "M": 5, "zero_coordinates": [[9, 2]], "reference_answer": 70}, "passing_reward_threshold": 1.0}} |
A **double cross** is a specific shape consisting of two horizontal and one vertical segments of `1`s. For example:
```
..........
....1..... ..1..
..11111... .111.
....1..... ..1..
.1111111.. 11111
....1..... ..1..
....1.....
..........
```
A valid double cross must satisfy the following condi... | {"environment": "DoubleCrossCounting", "config": {"seed": 43, "parameter": {"MAX_N_M": 10, "N": 5, "M": 7, "zero_coordinates": [[4, 1], [3, 2], [0, 6]], "reference_answer": 0}, "passing_reward_threshold": 1.0}} |
There are 13 generals numbered from 0 to 12. The medal requirements are: General 0 needs 19 medals of distinct types; General 1 needs 17 medals of distinct types; General 2 needs 2 medals of distinct types; General 3 needs 8 medals of distinct types; General 4 needs 10 medals of distinct types; General 5 needs 22 medal... | {"environment": "EmperorWorries", "config": {"seed": 40, "parameter": {"K": 6, "N": 13, "A": [19, 17, 2, 8, 10, 22, 21, 22, 7, 5, 25, 12, 9], "reference_answer": 43}, "passing_reward_threshold": 1.0}} |
There are 13 generals numbered from 0 to 12. The medal requirements are: General 0 needs 11 medals of distinct types; General 1 needs 8 medals of distinct types; General 2 needs 6 medals of distinct types; General 3 needs 13 medals of distinct types; General 4 needs 19 medals of distinct types; General 5 needs 23 medal... | {"environment": "EmperorWorries", "config": {"seed": 41, "parameter": {"K": 6, "N": 13, "A": [11, 8, 6, 13, 19, 23, 10, 18, 9, 13, 24, 25, 19], "reference_answer": 49}, "passing_reward_threshold": 1.0}} |
There are 12 generals numbered from 0 to 11. The medal requirements are: General 0 needs 1 medals of distinct types; General 1 needs 24 medals of distinct types; General 2 needs 9 medals of distinct types; General 3 needs 8 medals of distinct types; General 4 needs 8 medals of distinct types; General 5 needs 5 medals o... | {"environment": "EmperorWorries", "config": {"seed": 42, "parameter": {"K": 6, "N": 12, "A": [1, 24, 9, 8, 8, 5, 24, 4, 22, 24, 18, 3], "reference_answer": 46}, "passing_reward_threshold": 1.0}} |
There are 12 generals numbered from 0 to 11. The medal requirements are: General 0 needs 10 medals of distinct types; General 1 needs 23 medals of distinct types; General 2 needs 5 medals of distinct types; General 3 needs 15 medals of distinct types; General 4 needs 12 medals of distinct types; General 5 needs 22 meda... | {"environment": "EmperorWorries", "config": {"seed": 43, "parameter": {"K": 6, "N": 12, "A": [10, 23, 5, 15, 12, 22, 23, 4, 15, 20, 16, 20], "reference_answer": 45}, "passing_reward_threshold": 1.0}} |
There are 7 segments in the 2D plane, given as:
(8, 10)-(9, 1)
(4, 5)-(11, 11)
(11, 4)-(3, 13)
(6, 5)-(12, 8)
(14, 1)-(9, 12)
(3, 1)-(11, 4)
(10, 12)-(8, 14)
You may shoot at most 1 rays from the origin (0, 0) in any directions. Each segment is allowed to intersect with **at most one** of these rays. Please output the... | {"environment": "LASLaser", "config": {"seed": 40, "parameter": {"N": 7, "segments": [[8, 10, 9, 1], [4, 5, 11, 11], [11, 4, 3, 13], [6, 5, 12, 8], [14, 1, 9, 12], [3, 1, 11, 4], [10, 12, 8, 14]], "K": 1, "reference_answer": 5}, "passing_reward_threshold": 1.0}} |
There are 7 segments in the 2D plane, given as:
(7, 6)-(4, 3)
(7, 10)-(12, 5)
(9, 5)-(7, 14)
(12, 13)-(10, 1)
(13, 4)-(11, 14)
(1, 8)-(3, 3)
(12, 6)-(3, 5)
You may shoot at most 1 rays from the origin (0, 0) in any directions. Each segment is allowed to intersect with **at most one** of these rays. Please output the *... | {"environment": "LASLaser", "config": {"seed": 41, "parameter": {"N": 7, "segments": [[7, 6, 4, 3], [7, 10, 12, 5], [9, 5, 7, 14], [12, 13, 10, 1], [13, 4, 11, 14], [1, 8, 3, 3], [12, 6, 3, 5]], "K": 1, "reference_answer": 6}, "passing_reward_threshold": 1.0}} |
There are 7 segments in the 2D plane, given as:
(11, 2)-(1, 12)
(5, 4)-(4, 3)
(12, 2)-(11, 12)
(9, 2)-(10, 7)
(1, 1)-(2, 4)
(4, 9)-(10, 1)
(9, 4)-(12, 11)
You may shoot at most 1 rays from the origin (0, 0) in any directions. Each segment is allowed to intersect with **at most one** of these rays. Please output the **... | {"environment": "LASLaser", "config": {"seed": 42, "parameter": {"N": 7, "segments": [[11, 2, 1, 12], [5, 4, 4, 3], [12, 2, 11, 12], [9, 2, 10, 7], [1, 1, 2, 4], [4, 9, 10, 1], [9, 4, 12, 11]], "K": 1, "reference_answer": 5}, "passing_reward_threshold": 1.0}} |
There are 7 segments in the 2D plane, given as:
(1, 5)-(12, 13)
(3, 8)-(6, 11)
(12, 13)-(2, 8)
(10, 8)-(10, 1)
(9, 7)-(10, 6)
(10, 14)-(9, 13)
(7, 7)-(3, 1)
You may shoot at most 1 rays from the origin (0, 0) in any directions. Each segment is allowed to intersect with **at most one** of these rays. Please output the ... | {"environment": "LASLaser", "config": {"seed": 43, "parameter": {"N": 7, "segments": [[1, 5, 12, 13], [3, 8, 6, 11], [12, 13, 2, 8], [10, 8, 10, 1], [9, 7, 10, 6], [10, 14, 9, 13], [7, 7, 3, 1]], "K": 1, "reference_answer": 3}, "passing_reward_threshold": 1.0}} |
You are given an array A of 9 integers: A[0]=9 A[1]=8 A[2]=0 A[3]=3 A[4]=4 A[5]=3 A[6]=2 A[7]=5 A[8]=4
Initially, the entire array is one single block. Let S = 0. You need to perform the following operation exactly 5 times:
- Choose a position `i` such that A[i] and A[i + 1] are still in the same block.
- Split the bl... | {"environment": "MaxDifferentGroupPairDivision", "config": {"seed": 40, "parameter": {"N": 9, "K": 5, "A": [9, 8, 0, 3, 4, 3, 2, 5, 4], "gold_answer": 592, "reference_answer": "0 2 4 6 7"}, "passing_reward_threshold": 1.0}} |
You are given an array A of 9 integers: A[0]=5 A[1]=3 A[2]=2 A[3]=6 A[4]=9 A[5]=4 A[6]=8 A[7]=4 A[8]=6
Initially, the entire array is one single block. Let S = 0. You need to perform the following operation exactly 5 times:
- Choose a position `i` such that A[i] and A[i + 1] are still in the same block.
- Split the bl... | {"environment": "MaxDifferentGroupPairDivision", "config": {"seed": 41, "parameter": {"N": 9, "K": 5, "A": [5, 3, 2, 6, 9, 4, 8, 4, 6], "gold_answer": 910, "reference_answer": "1 3 4 5 6"}, "passing_reward_threshold": 1.0}} |
You are given an array A of 9 integers: A[0]=1 A[1]=0 A[2]=4 A[3]=3 A[4]=3 A[5]=2 A[6]=1 A[7]=8 A[8]=1
Initially, the entire array is one single block. Let S = 0. You need to perform the following operation exactly 7 times:
- Choose a position `i` such that A[i] and A[i + 1] are still in the same block.
- Split the bl... | {"environment": "MaxDifferentGroupPairDivision", "config": {"seed": 42, "parameter": {"N": 9, "K": 7, "A": [1, 0, 4, 3, 3, 2, 1, 8, 1], "gold_answer": 212, "reference_answer": "1 2 3 4 5 6 7"}, "passing_reward_threshold": 1.0}} |
You are given an array A of 9 integers: A[0]=4 A[1]=2 A[2]=7 A[3]=5 A[4]=1 A[5]=7 A[6]=9 A[7]=7 A[8]=9
Initially, the entire array is one single block. Let S = 0. You need to perform the following operation exactly 2 times:
- Choose a position `i` such that A[i] and A[i + 1] are still in the same block.
- Split the bl... | {"environment": "MaxDifferentGroupPairDivision", "config": {"seed": 43, "parameter": {"N": 9, "K": 2, "A": [4, 2, 7, 5, 1, 7, 9, 7, 9], "gold_answer": 866, "reference_answer": "3 6"}, "passing_reward_threshold": 1.0}} |
You are given an **undirected graph** with 16 vertices labeled from `0` to `15`. The graph contains the following undirected edges (no repeated edges):
(5, 14)
(0, 1)
(3, 12)
(6, 9)
(2, 5)
(4, 10)
(8, 14)
(3, 14)
(12, 13)
(0, 11)
(10, 11)
(8, 11)
(2, 3)
(10, 13)
(1, 15)
(9, 15)
(4, 7)
Please count the number of path... | {"environment": "Path_NoGoingBack_Counting", "config": {"seed": 40, "parameter": {"MAX_M": 20, "M": 17, "N": 16, "T": 4175, "edges": [[5, 14], [0, 1], [3, 12], [6, 9], [2, 5], [4, 10], [8, 14], [3, 14], [12, 13], [0, 11], [10, 11], [8, 11], [2, 3], [10, 13], [1, 15], [9, 15], [4, 7]], "reference_answer": 6702}, "passin... |
You are given an **undirected graph** with 11 vertices labeled from `0` to `10`. The graph contains the following undirected edges (no repeated edges):
(0, 7)
(5, 7)
(3, 5)
(4, 6)
(2, 5)
(0, 9)
(4, 8)
(3, 8)
(4, 5)
(9, 10)
(1, 10)
(5, 9)
(2, 6)
(0, 8)
(2, 10)
Please count the number of paths from vertex `0` to verte... | {"environment": "Path_NoGoingBack_Counting", "config": {"seed": 41, "parameter": {"MAX_M": 20, "M": 15, "N": 11, "T": 946, "edges": [[0, 7], [5, 7], [3, 5], [4, 6], [2, 5], [0, 9], [4, 8], [3, 8], [4, 5], [9, 10], [1, 10], [5, 9], [2, 6], [0, 8], [2, 10]], "reference_answer": 1242}, "passing_reward_threshold": 1.0}} |
You are given an **undirected graph** with 4 vertices labeled from `0` to `3`. The graph contains the following undirected edges (no repeated edges):
(0, 2)
(0, 1)
(1, 3)
(2, 3)
(0, 3)
(1, 2)
Please count the number of paths from vertex `0` to vertex `3` that satisfy the following conditions:
- The path has exactly ... | {"environment": "Path_NoGoingBack_Counting", "config": {"seed": 42, "parameter": {"MAX_M": 20, "M": 6, "N": 4, "T": 9, "edges": [[0, 2], [0, 1], [1, 3], [2, 3], [0, 3], [1, 2]], "reference_answer": 190}, "passing_reward_threshold": 1.0}} |
You are given an **undirected graph** with 5 vertices labeled from `0` to `4`. The graph contains the following undirected edges (no repeated edges):
(0, 1)
(0, 4)
(2, 4)
(2, 3)
Please count the number of paths from vertex `0` to vertex `4` that satisfy the following conditions:
- The path has exactly 10 edges.
- Yo... | {"environment": "Path_NoGoingBack_Counting", "config": {"seed": 43, "parameter": {"MAX_M": 20, "M": 4, "N": 5, "T": 10, "edges": [[0, 1], [0, 4], [2, 4], [2, 3]], "reference_answer": 0}, "passing_reward_threshold": 1.0}} |
You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices labeled from `1` to `9`. It contains the following 8 undirected edges:
3 5
5 7
2 7
7 8
1 5
4 9
5 9
5 6
You are allowed to add 1 arbitrary edges to the tree. Each added edge can connect any two existing vertices (including poss... | {"environment": "Patrol", "config": {"seed": 2614, "parameter": {"N": 9, "edges": [[3, 5], [5, 7], [2, 7], [7, 8], [1, 5], [4, 9], [5, 9], [5, 6]], "K": 1, "reference_answer": 13}, "passing_reward_threshold": 1.0}} |
You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices labeled from `1` to `9`. It contains the following 8 undirected edges:
3 6
2 4
3 5
1 3
2 6
2 9
2 8
6 7
You are allowed to add 1 arbitrary edges to the tree. Each added edge can connect any two existing vertices (including poss... | {"environment": "Patrol", "config": {"seed": 2615, "parameter": {"N": 9, "edges": [[3, 6], [2, 4], [3, 5], [1, 3], [2, 6], [2, 9], [2, 8], [6, 7]], "K": 1, "reference_answer": 13}, "passing_reward_threshold": 1.0}} |
You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices labeled from `1` to `9`. It contains the following 8 undirected edges:
2 9
2 5
1 8
1 2
3 5
4 5
2 7
3 6
You are allowed to add 2 arbitrary edges to the tree. Each added edge can connect any two existing vertices (including poss... | {"environment": "Patrol", "config": {"seed": 2616, "parameter": {"N": 9, "edges": [[2, 9], [2, 5], [1, 8], [1, 2], [3, 5], [4, 5], [2, 7], [3, 6]], "K": 2, "reference_answer": 11}, "passing_reward_threshold": 1.0}} |
You are given a **tree** (i.e., a connected undirected graph with no cycles) with 9 vertices labeled from `1` to `9`. It contains the following 8 undirected edges:
5 8
5 7
1 7
3 5
5 6
1 4
2 4
5 9
You are allowed to add 1 arbitrary edges to the tree. Each added edge can connect any two existing vertices (including poss... | {"environment": "Patrol", "config": {"seed": 2617, "parameter": {"N": 9, "edges": [[5, 8], [5, 7], [1, 7], [3, 5], [5, 6], [1, 4], [2, 4], [5, 9]], "K": 1, "reference_answer": 12}, "passing_reward_threshold": 1.0}} |
You are given a **positive integer** `73`.
Every positive integer can be represented as a **sum of powers of 2**. For example:
137 = 2^7 + 2^3 + 2^0
We adopt the following format:
- A power expression like a^b should be written as `a(b)`
- So, 137 can be written as: `2(7)+2(3)+2(0)`
Now, each exponent (like `7`, `3`... | {"environment": "PowerNest", "config": {"seed": 2900, "parameter": {"max_number": 128, "number": 73, "reference_answer": "2(2(2)+2)+2(2+2(0))+2(0)"}, "passing_reward_threshold": 1.0}} |
You are given a **positive integer** `59`.
Every positive integer can be represented as a **sum of powers of 2**. For example:
137 = 2^7 + 2^3 + 2^0
We adopt the following format:
- A power expression like a^b should be written as `a(b)`
- So, 137 can be written as: `2(7)+2(3)+2(0)`
Now, each exponent (like `7`, `3`... | {"environment": "PowerNest", "config": {"seed": 2902, "parameter": {"max_number": 128, "number": 59, "reference_answer": "2(2(2)+2(0))+2(2(2))+2(2+2(0))+2+2(0)"}, "passing_reward_threshold": 1.0}} |
You are given a **positive integer** `95`.
Every positive integer can be represented as a **sum of powers of 2**. For example:
137 = 2^7 + 2^3 + 2^0
We adopt the following format:
- A power expression like a^b should be written as `a(b)`
- So, 137 can be written as: `2(7)+2(3)+2(0)`
Now, each exponent (like `7`, `3`... | {"environment": "PowerNest", "config": {"seed": 2904, "parameter": {"max_number": 128, "number": 95, "reference_answer": "2(2(2)+2)+2(2(2))+2(2+2(0))+2(2)+2+2(0)"}, "passing_reward_threshold": 1.0}} |
You are given a **positive integer** `32`.
Every positive integer can be represented as a **sum of powers of 2**. For example:
137 = 2^7 + 2^3 + 2^0
We adopt the following format:
- A power expression like a^b should be written as `a(b)`
- So, 137 can be written as: `2(7)+2(3)+2(0)`
Now, each exponent (like `7`, `3`... | {"environment": "PowerNest", "config": {"seed": 2906, "parameter": {"max_number": 128, "number": 32, "reference_answer": "2(2(2)+2(0))"}, "passing_reward_threshold": 1.0}} |
You are given two arrays `T` and `D`, each containing 8 integers:
T[1]=8 D[1]=8
T[2]=1 D[2]=1
T[3]=4 D[3]=3
T[4]=5 D[4]=1
T[5]=4 D[5]=4
T[6]=3 D[6]=8
T[7]=6 D[7]=1
T[8]=5 D[8]=3
Please output **a permutation of 1 to 8**, denoted as p[1], p[2], ..., p[8] (8 integers in one line) with adjacent numbers separated by space... | {"environment": "ProtectingFlowers", "config": {"seed": 40, "parameter": {"N": 8, "T": [8, 1, 4, 5, 4, 3, 6, 5], "D": [8, 1, 3, 1, 4, 8, 1, 3], "gold_answer": 246}, "passing_reward_threshold": 1.0}} |
You are given two arrays `T` and `D`, each containing 8 integers:
T[1]=7 D[1]=1
T[2]=6 D[2]=4
T[3]=4 D[3]=1
T[4]=3 D[4]=8
T[5]=7 D[5]=3
T[6]=5 D[6]=3
T[7]=5 D[7]=6
T[8]=7 D[8]=3
Please output **a permutation of 1 to 8**, denoted as p[1], p[2], ..., p[8] (8 integers in one line) with adjacent numbers separated by space... | {"environment": "ProtectingFlowers", "config": {"seed": 41, "parameter": {"N": 8, "T": [7, 6, 4, 3, 7, 5, 5, 7], "D": [1, 4, 1, 8, 3, 3, 6, 3], "gold_answer": 297}, "passing_reward_threshold": 1.0}} |
You are given two arrays `T` and `D`, each containing 8 integers:
T[1]=2 D[1]=7
T[2]=1 D[2]=1
T[3]=5 D[3]=1
T[4]=4 D[4]=2
T[5]=4 D[5]=4
T[6]=3 D[6]=4
T[7]=2 D[7]=1
T[8]=2 D[8]=4
Please output **a permutation of 1 to 8**, denoted as p[1], p[2], ..., p[8] (8 integers in one line) with adjacent numbers separated by space... | {"environment": "ProtectingFlowers", "config": {"seed": 42, "parameter": {"N": 8, "T": [2, 1, 5, 4, 4, 3, 2, 2], "D": [7, 1, 1, 2, 4, 4, 1, 4], "gold_answer": 121}, "passing_reward_threshold": 1.0}} |
You are given two arrays `T` and `D`, each containing 8 integers:
T[1]=1 D[1]=1
T[2]=5 D[2]=7
T[3]=3 D[3]=6
T[4]=8 D[4]=7
T[5]=6 D[5]=7
T[6]=2 D[6]=3
T[7]=8 D[7]=1
T[8]=8 D[8]=2
Please output **a permutation of 1 to 8**, denoted as p[1], p[2], ..., p[8] (8 integers in one line) with adjacent numbers separated by space... | {"environment": "ProtectingFlowers", "config": {"seed": 43, "parameter": {"N": 8, "T": [1, 5, 3, 8, 6, 2, 8, 8], "D": [1, 7, 6, 7, 7, 3, 1, 2], "gold_answer": 332}, "passing_reward_threshold": 1.0}} |
There is an array X of length 8. Initially, X is: X[0]=30 X[1]=3 X[2]=16 X[3]=19 X[4]=14 X[5]=9 X[6]=23 X[7]=18
You can perform the following operation at most 115 times: pick an arbitrary index i and decrease X[i] by 1 (i.e., X[i] -= 1); at the end, you must ensure that there exists at least one index i such that X[i]... | {"environment": "STUWell", "config": {"seed": 40, "parameter": {"N": 8, "X": [30, 3, 16, 19, 14, 9, 23, 18], "M": 115, "reference_answer": 1}, "passing_reward_threshold": 1.0}} |
There is an array X of length 8. Initially, X is: X[0]=25 X[1]=22 X[2]=15 X[3]=11 X[4]=25 X[5]=19 X[6]=18 X[7]=25
You can perform the following operation at most 158 times: pick an arbitrary index i and decrease X[i] by 1 (i.e., X[i] -= 1); at the end, you must ensure that there exists at least one index i such that X[... | {"environment": "STUWell", "config": {"seed": 41, "parameter": {"N": 8, "X": [25, 22, 15, 11, 25, 19, 18, 25], "M": 158, "reference_answer": 1}, "passing_reward_threshold": 1.0}} |
There is an array X of length 8. Initially, X is: X[0]=8 X[1]=2 X[2]=18 X[3]=16 X[4]=15 X[5]=9 X[6]=7 X[7]=6
You can perform the following operation at most 77 times: pick an arbitrary index i and decrease X[i] by 1 (i.e., X[i] -= 1); at the end, you must ensure that there exists at least one index i such that X[i] = 0... | {"environment": "STUWell", "config": {"seed": 42, "parameter": {"N": 8, "X": [8, 2, 18, 16, 15, 9, 7, 6], "M": 77, "reference_answer": 1}, "passing_reward_threshold": 1.0}} |
There is an array X of length 8. Initially, X is: X[0]=3 X[1]=19 X[2]=10 X[3]=30 X[4]=24 X[5]=7 X[6]=30 X[7]=32
You can perform the following operation at most 7 times: pick an arbitrary index i and decrease X[i] by 1 (i.e., X[i] -= 1); at the end, you must ensure that there exists at least one index i such that X[i] =... | {"environment": "STUWell", "config": {"seed": 43, "parameter": {"N": 8, "X": [3, 19, 10, 30, 24, 7, 30, 32], "M": 7, "reference_answer": 20}, "passing_reward_threshold": 1.0}} |
Please find 8 **distinct positive integers** such that the sums of all 8 * (8 - 1) / 2 distinct pairs among them (in any order) are exactly: 19, 5, 10, 15, 17, 9, 19, 8, 16, 12, 13, 4, 14, 14, 13, 27, 6, 15, 18, 24, 20, 21, 25, 13, 16, 11, 22, 7
Output these 8 integers, separated by spaces. | {"environment": "SquSquarks", "config": {"seed": 40, "parameter": {"N": 8, "reference_answer": "15 10 9 1 4 5 12 3", "sums": [19, 5, 10, 15, 17, 9, 19, 8, 16, 12, 13, 4, 14, 14, 13, 27, 6, 15, 18, 24, 20, 21, 25, 13, 16, 11, 22, 7]}, "passing_reward_threshold": 1.0}} |
Please find 8 **distinct positive integers** such that the sums of all 8 * (8 - 1) / 2 distinct pairs among them (in any order) are exactly: 22, 13, 14, 12, 14, 16, 20, 7, 17, 8, 19, 13, 11, 9, 13, 18, 16, 15, 23, 11, 17, 10, 19, 10, 16, 12, 15, 9
Output these 8 integers, separated by spaces. | {"environment": "SquSquarks", "config": {"seed": 41, "parameter": {"N": 8, "reference_answer": "13 6 4 3 7 10 5 9", "sums": [22, 13, 14, 12, 14, 16, 20, 7, 17, 8, 19, 13, 11, 9, 13, 18, 16, 15, 23, 11, 17, 10, 19, 10, 16, 12, 15, 9]}, "passing_reward_threshold": 1.0}} |
Please find 8 **distinct positive integers** such that the sums of all 8 * (8 - 1) / 2 distinct pairs among them (in any order) are exactly: 17, 3, 7, 5, 26, 19, 18, 17, 30, 16, 28, 15, 4, 20, 6, 8, 15, 13, 6, 18, 5, 16, 17, 21, 9, 14, 19, 7
Output these 8 integers, separated by spaces. | {"environment": "SquSquarks", "config": {"seed": 42, "parameter": {"N": 8, "reference_answer": "4 1 12 5 16 14 3 2", "sums": [17, 3, 7, 5, 26, 19, 18, 17, 30, 16, 28, 15, 4, 20, 6, 8, 15, 13, 6, 18, 5, 16, 17, 21, 9, 14, 19, 7]}, "passing_reward_threshold": 1.0}} |
Please find 8 **distinct positive integers** such that the sums of all 8 * (8 - 1) / 2 distinct pairs among them (in any order) are exactly: 22, 13, 17, 14, 18, 5, 10, 8, 19, 15, 18, 11, 14, 19, 9, 8, 21, 29, 28, 11, 16, 25, 18, 7, 24, 20, 21, 15
Output these 8 integers, separated by spaces. | {"environment": "SquSquarks", "config": {"seed": 43, "parameter": {"N": 8, "reference_answer": "2 5 12 13 3 8 6 16", "sums": [22, 13, 17, 14, 18, 5, 10, 8, 19, 15, 18, 11, 14, 19, 9, 8, 21, 29, 28, 11, 16, 25, 18, 7, 24, 20, 21, 15]}, "passing_reward_threshold": 1.0}} |
You are given a **tree** with 8 vertices labeled from `1` to `8`, where vertex `1` is the **root** of the tree. Each vertex (except the root `1`) has a parent, specified as follows:
parent[4]=1
parent[3]=1
parent[8]=4
parent[2]=3
parent[7]=8
parent[6]=1
parent[5]=2
Initially, **all vertices are uncolored**. In each st... | {"environment": "TreeElimination_Expectation", "config": {"seed": 40, "parameter": {"N": 8, "parents": [[1, 4], [1, 3], [4, 8], [3, 2], [8, 7], [1, 6], [2, 5]], "reference_answer": 791666677}, "passing_reward_threshold": 1.0}} |
You are given a **tree** with 8 vertices labeled from `1` to `8`, where vertex `1` is the **root** of the tree. Each vertex (except the root `1`) has a parent, specified as follows:
parent[2]=1
parent[7]=2
parent[8]=7
parent[6]=1
parent[3]=2
parent[4]=3
parent[5]=4
Initially, **all vertices are uncolored**. In each st... | {"environment": "TreeElimination_Expectation", "config": {"seed": 41, "parameter": {"N": 8, "parents": [[1, 2], [2, 7], [7, 8], [1, 6], [2, 3], [3, 4], [4, 5]], "reference_answer": 625000009}, "passing_reward_threshold": 1.0}} |
You are given a **tree** with 8 vertices labeled from `1` to `8`, where vertex `1` is the **root** of the tree. Each vertex (except the root `1`) has a parent, specified as follows:
parent[3]=1
parent[5]=1
parent[6]=5
parent[4]=1
parent[8]=4
parent[2]=6
parent[7]=1
Initially, **all vertices are uncolored**. In each st... | {"environment": "TreeElimination_Expectation", "config": {"seed": 42, "parameter": {"N": 8, "parents": [[1, 3], [1, 5], [5, 6], [1, 4], [4, 8], [6, 2], [1, 7]], "reference_answer": 458333342}, "passing_reward_threshold": 1.0}} |
You are given a **tree** with 8 vertices labeled from `1` to `8`, where vertex `1` is the **root** of the tree. Each vertex (except the root `1`) has a parent, specified as follows:
parent[7]=1
parent[8]=7
parent[6]=8
parent[5]=1
parent[3]=5
parent[4]=6
parent[2]=5
Initially, **all vertices are uncolored**. In each st... | {"environment": "TreeElimination_Expectation", "config": {"seed": 43, "parameter": {"N": 8, "parents": [[1, 7], [7, 8], [8, 6], [1, 5], [5, 3], [6, 4], [5, 2]], "reference_answer": 541666675}, "passing_reward_threshold": 1.0}} |
You are given a set of integers: 11 10 2 5 6 13 4 7 15
Please compute the number of set pairs (S, T) such that:
1. S and T are disjoint subsets of the given set.
2. For every x in S and y in T, gcd(x, y) = 1 (i.e., there is no pair with gcd > 1). | {"environment": "TwoSet_AllCoprime_Counting", "config": {"seed": 40, "parameter": {"N": 16, "set": [11, 10, 2, 5, 6, 13, 4, 7, 15], "reference_answer": 4131}, "passing_reward_threshold": 1.0}} |
You are given a set of integers: 7 5 4 8 11 6 10 12
Please compute the number of set pairs (S, T) such that:
1. S and T are disjoint subsets of the given set.
2. For every x in S and y in T, gcd(x, y) = 1 (i.e., there is no pair with gcd > 1). | {"environment": "TwoSet_AllCoprime_Counting", "config": {"seed": 41, "parameter": {"N": 16, "set": [7, 5, 4, 8, 11, 6, 10, 12], "reference_answer": 1413}, "passing_reward_threshold": 1.0}} |
You are given a set of integers: 3 2 13 6 5 12 4 16 7 8 14 15
Please compute the number of set pairs (S, T) such that:
1. S and T are disjoint subsets of the given set.
2. For every x in S and y in T, gcd(x, y) = 1 (i.e., there is no pair with gcd > 1). | {"environment": "TwoSet_AllCoprime_Counting", "config": {"seed": 42, "parameter": {"N": 16, "set": [3, 2, 13, 6, 5, 12, 4, 16, 7, 8, 14, 15], "reference_answer": 22407}, "passing_reward_threshold": 1.0}} |
You are given a set of integers: 6 13
Please compute the number of set pairs (S, T) such that:
1. S and T are disjoint subsets of the given set.
2. For every x in S and y in T, gcd(x, y) = 1 (i.e., there is no pair with gcd > 1). | {"environment": "TwoSet_AllCoprime_Counting", "config": {"seed": 43, "parameter": {"N": 16, "set": [6, 13], "reference_answer": 9}, "passing_reward_threshold": 1.0}} |
You are given 8 items labeled from `0` to `7`. Each item has a base value W[i] and a diminishing factor R[i]. The list of values and diminishing factors is given as:
W[0]=29 R[0]=8
W[1]=2 R[1]=1
W[2]=15 R[2]=3
W[3]=18 R[3]=1
W[4]=13 R[4]=4
W[5]=8 R[5]=8
W[6]=22 R[6]=1
W[7]=17 R[7]=3
You must select a sequence of **dis... | {"environment": "ValueDiminishingSelection", "config": {"seed": 40, "parameter": {"N": 8, "W": [29, 2, 15, 18, 13, 8, 22, 17], "R": [8, 1, 3, 1, 4, 8, 1, 3], "gold_answer": 86}, "passing_reward_threshold": 1.0}} |
You are given 8 items labeled from `0` to `7`. Each item has a base value W[i] and a diminishing factor R[i]. The list of values and diminishing factors is given as:
W[0]=24 R[0]=1
W[1]=21 R[1]=4
W[2]=14 R[2]=1
W[3]=10 R[3]=8
W[4]=24 R[4]=3
W[5]=18 R[5]=3
W[6]=17 R[6]=6
W[7]=24 R[7]=3
You must select a sequence of **d... | {"environment": "ValueDiminishingSelection", "config": {"seed": 41, "parameter": {"N": 8, "W": [24, 21, 14, 10, 24, 18, 17, 24], "R": [1, 4, 1, 8, 3, 3, 6, 3], "gold_answer": 100}, "passing_reward_threshold": 1.0}} |
You are given 8 items labeled from `0` to `7`. Each item has a base value W[i] and a diminishing factor R[i]. The list of values and diminishing factors is given as:
W[0]=7 R[0]=7
W[1]=1 R[1]=1
W[2]=17 R[2]=1
W[3]=15 R[3]=2
W[4]=14 R[4]=4
W[5]=8 R[5]=4
W[6]=6 R[6]=1
W[7]=5 R[7]=4
You must select a sequence of **distin... | {"environment": "ValueDiminishingSelection", "config": {"seed": 42, "parameter": {"N": 8, "W": [7, 1, 17, 15, 14, 8, 6, 5], "R": [7, 1, 1, 2, 4, 4, 1, 4], "gold_answer": 45}, "passing_reward_threshold": 1.0}} |
You are given 8 items labeled from `0` to `7`. Each item has a base value W[i] and a diminishing factor R[i]. The list of values and diminishing factors is given as:
W[0]=2 R[0]=1
W[1]=18 R[1]=7
W[2]=9 R[2]=6
W[3]=29 R[3]=7
W[4]=23 R[4]=7
W[5]=6 R[5]=3
W[6]=29 R[6]=1
W[7]=31 R[7]=2
You must select a sequence of **dist... | {"environment": "ValueDiminishingSelection", "config": {"seed": 43, "parameter": {"N": 8, "W": [2, 18, 9, 29, 23, 6, 29, 31], "R": [1, 7, 6, 7, 7, 3, 1, 2], "gold_answer": 99}, "passing_reward_threshold": 1.0}} |
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