index int64 | sample_id int64 | data_source string | prompt string | response string | rewards float64 | metadata string | answer unknown |
|---|---|---|---|---|---|---|---|
1,272 | 0 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 15
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's see. I need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 15, and a × b is divisible by a + b. Hmm. So, the condition is that (a × b) is divisible by (a + b). Let me think about how to approach this.
First, let me recall that if a number X is divisible by Y, then X/Y is an integer. So, in th... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 10, "parameter": {"MAX_N": 16, "N": 15, "reference_answer": 4}, "passing_reward_threshold": 1.0}} | 4 |
1,272 | 1 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 15
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's see. I need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 15, and a × b is divisible by a + b. Hmm, so the condition is that (a*b) is divisible by (a + b).
First, let me understand what this means. If a*b is divisible by a + b, then there exists some integer k such that a*b = k*(a + b). Alt... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 10, "parameter": {"MAX_N": 16, "N": 15, "reference_answer": 4}, "passing_reward_threshold": 1.0}} | 4 |
1,431 | 0 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 13
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's try to solve this problem. So, we need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 13, and a × b is divisible by a + b. Hmm, let's think step by step.
First, let me understand the condition. The problem says that a × b is divisible by a + b. In mathematical terms, that means (a × b) / (a +... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 11, "parameter": {"MAX_N": 16, "N": 13, "reference_answer": 3}, "passing_reward_threshold": 1.0}} | 3 |
1,431 | 1 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 13
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's tackle this problem. So, I need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 13, and a × b is divisible by a + b. Hmm, let's think about how to approach this.
First, the condition is that a × b is divisible by a + b. In mathematical terms, that means (a × b) mod (a + b) = 0. So, a + b divid... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 11, "parameter": {"MAX_N": 16, "N": 13, "reference_answer": 3}, "passing_reward_threshold": 1.0}} | 3 |
1,590 | 0 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 13
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's try to solve this problem. So, we need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 13, and a × b is divisible by a + b. Hmm, let me think about how to approach this.
First, the condition is that a × b is divisible by a + b. That means when you divide a × b by a + b, there's no remainder. S... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 12, "parameter": {"MAX_N": 16, "N": 13, "reference_answer": 3}, "passing_reward_threshold": 1.0}} | 3 |
1,590 | 1 | AddMultiple_Divisible_Counting | Please compute the number of pairs (a, b) such that:
- 1 ≤ a < b ≤ 13
- a × b is divisible by a + b
**Output Format:** Your final answer should be a single integer — the number of such pairs (a, b). | <think>
Okay, let's try to figure out how to solve this problem. The task is to find the number of pairs (a, b) where 1 ≤ a < b ≤ 13, and a × b is divisible by a + b. Hmm, let's break this down.
First, I need to understand the condition: a × b is divisible by a + b. That means when you divide a × b by a + b, there's n... | -1 | {"environment": "AddMultiple_Divisible_Counting", "config": {"seed": 12, "parameter": {"MAX_N": 16, "N": 13, "reference_answer": 3}, "passing_reward_threshold": 1.0}} | 3 |
1,749 | 0 | AddMultiple_Divisible_Counting | "Please compute the number of pairs (a, b) such that:\n- 1 ≤ a < b ≤ 10\n- a × b is divisible b(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem. So, I need to find the number of pairs (a, b) where(...TRUNCATED) | -1 | "{\"environment\": \"AddMultiple_Divisible_Counting\", \"config\": {\"seed\": 13, \"parameter\": {\"(...TRUNCATED) | 1 |
1,749 | 1 | AddMultiple_Divisible_Counting | "Please compute the number of pairs (a, b) such that:\n- 1 ≤ a < b ≤ 10\n- a × b is divisible b(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem. The task is to find the number of pairs (a, b) wher(...TRUNCATED) | -1 | "{\"environment\": \"AddMultiple_Divisible_Counting\", \"config\": {\"seed\": 13, \"parameter\": {\"(...TRUNCATED) | 1 |
1,908 | 0 | AddMultiple_Divisible_Counting | "Please compute the number of pairs (a, b) such that:\n- 1 ≤ a < b ≤ 7\n- a × b is divisible by(...TRUNCATED) | "<think>\nOkay, let's see. I need to find the number of pairs (a, b) where 1 ≤ a < b ≤ 7, and a (...TRUNCATED) | -1 | "{\"environment\": \"AddMultiple_Divisible_Counting\", \"config\": {\"seed\": 14, \"parameter\": {\"(...TRUNCATED) | 1 |
1,908 | 1 | AddMultiple_Divisible_Counting | "Please compute the number of pairs (a, b) such that:\n- 1 ≤ a < b ≤ 7\n- a × b is divisible by(...TRUNCATED) | "<think>\nOkay, let's try to solve this problem. The task is to find the number of pairs (a, b) wher(...TRUNCATED) | -1 | "{\"environment\": \"AddMultiple_Divisible_Counting\", \"config\": {\"seed\": 14, \"parameter\": {\"(...TRUNCATED) | 1 |
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