| [{"task_id": "mmlu-7313", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] If both parents are affected with the same autosomal recessive disorder then the probability that each of their children will be affected equals ___.\nA) 1 in 4\nB) 1 in 2\nC) 2 in 3\nD) 1\n\nAnswer with the letter only.", "response": "D", "cost_usd": 1.02e-05, "tokens_in": 72, "tokens_out": 5, "latency_s": 1.526}, {"task_id": "mmlu-1621", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A step-up transformer in an electrical circuit can step up\nA) voltage\nB) energy\nC) Both of these\nD) Neither of these\n\nAnswer with the letter only.", "response": "A", "cost_usd": 7.8e-06, "tokens_in": 48, "tokens_out": 5, "latency_s": 1.037}, {"task_id": "gsm8k-954", "model": "openai/gpt-5.6-luna", "prompt": "Jonathan has 2/3 as many measuring spoons as measuring cups. If he has two dozen cups and gifts Pedro 6 measuring spoons for his birthday, calculate the total number of utensils Jonathan has remaining.\n\nReason step by step, then give the final answer as a single number.", "response": "Jonathan has \\(24\\) measuring cups.\n\nMeasuring spoons: \\(\\frac{2}{3}\\times 24=16\\).\n\nAfter gifting \\(6\\) spoons: \\(16-6=10\\).\n\nTotal utensils remaining: \\(24+10=34\\).\n\n34", "cost_usd": 8.26e-05, "tokens_in": 64, "tokens_out": 127, "latency_s": 3.191}, {"task_id": "gsm8k-520", "model": "openai/gpt-5.6-luna", "prompt": "Martha is knitting winter wear for her 3 grandchildren. They're triplets, so they're all the same size. She wants to make a hat, scarf, sweater, mittens, and socks for each of them. It takes 2 skeins of wool to make a hat, 4 for a scarf, 12 for a sweater, 1 for a pair of mittens, and 2 for a pair of socks. How many skeins of wool will she need to buy?\n\nReason step by step, then give the final answer as a single number.", "response": "Each grandchild needs:\n\n2 + 4 + 12 + 1 + 2 = 21 skeins\n\nFor 3 grandchildren:\n\n21 \u00d7 3 = 63\n\n63", "cost_usd": 6.9e-05, "tokens_in": 120, "tokens_out": 95, "latency_s": 5.387}, {"task_id": "lcb-abc400_a", "model": "openai/gpt-5.6-luna", "prompt": "In the ceremony commemorating ABC400, we want to arrange 400 people in a rectangular formation of A rows and B columns without any gaps.\nYou are given a positive integer A. Print the value of a positive integer B for which such an arrangement is possible. If there is no such positive integer B, print -1.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA\n\nOutput\n\nPrint the value of B or -1 as specified by the problem statement.\n\nConstraints\n\n\n- A is an integer between 1 and 400, inclusive.\n\nSample Input 1\n\n10\n\nSample Output 1\n\n40\r\n\nWe can arrange 400 people in 10 rows and 40 columns.\n\nSample Input 2\n\n11\n\nSample Output 2\n\n-1\n\nSample Input 3\n\n400\n\nSample Output 3\n\n1\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.", "response": "a = int(input())\nprint(400 // a if 400 % a == 0 else -1)\n", "cost_usd": 3.68e-05, "tokens_in": 212, "tokens_out": 26, "latency_s": 0.676}, {"task_id": "lcb-abc390_d", "model": "openai/gpt-5.6-luna", "prompt": "There are N bags, labeled bag 1, bag 2, \\ldots, bag N.\r\nBag i (1 \\leq i \\leq N) contains A_i stones.\nTakahashi can perform the following operation any number of times, possibly zero:\n\nChoose two bags A and B, and move all stones from bag A into bag B.\n\nFind the number of different possible values for the following after repeating the operation.\n\n- B_1 \\oplus B_2 \\oplus \\cdots \\oplus B_N, where B_i is the final number of stones in bag i.\r\nHere, \\oplus denotes bitwise XOR.\n\n\nAbout bitwise XOR\r\nFor non-negative integers a and b, the bitwise XOR a \\oplus b is defined as follows:\r\n\r\n\r\nIn the binary representation of a \\oplus b, the digit in the 2^k place (k \\ge 0) is 1 if and only if exactly one of the digits in the 2^k place of a and b is 1; otherwise, it is 0.\r\n\r\n\r\nFor example, 3 \\oplus 5 = 6 (in binary, 011 \\oplus 101 = 110).\r\nIn general, for k non-negative integers x_1, x_2, \\ldots, x_k, their bitwise XOR x_1 \\oplus x_2 \\oplus \\cdots \\oplus x_k is defined as (\\cdots((x_1 \\oplus x_2) \\oplus x_3) \\oplus \\cdots) \\oplus x_k, which does not depend on the order of x_1, x_2, \\ldots, x_k.\r\n\nIt can be proved that under the constraints of this problem, the number of possible values is finite.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nPrint the number of different possible values for B_1 \\oplus B_2 \\oplus \\cdots \\oplus B_N after repeating the operation.\n\nConstraints\n\n\n- 2 \\leq N \\leq 12\n- 1 \\leq A_i \\leq 10^{17}\n- All input values are integers.\n\nSample Input 1\n\n3\r\n2 5 7\n\nSample Output 1\n\n3\r\n\nFor example, if Takahashi chooses bags 1 and 3 for the operation, then the numbers of stones in bags 1, 2, 3 become 0, 5, 9.\r\nIf he stops at this point, the XOR is 0 \\oplus 5 \\oplus 9 = 12.\nThe other possible XOR values after repeating the operation are 0 and 14.\r\nTherefore, the possible values are 0, 12, 14; there are three values, so the output is 3.\n\nSample Input 2\n\n2\r\n100000000000000000 100000000000000000\n\nSample Output 2\n\n2\n\nSample Input 3\n\n6\r\n71 74 45 34 31 60\n\nSample Output 3\n\n84\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.", "response": "import sys\n\ndef main():\n input = sys.stdin.readline\n n = int(input())\n a = list(map(int, input().split()))\n\n size = 1 << n\n subset_sum = [0] * size\n for mask in range(1, size):\n bit = mask & -mask\n i = bit.bit_length() - 1\n subset_sum[mask] = subset_sum[mask ^ bit] + a[i]\n\n choices = [[] for _ in range(size)]\n for mask in range(1, size):\n first = mask & -mask\n rest = mask ^ first\n sub = rest\n lst = choices[mask]\n while True:\n block = sub | first\n lst.append(block)\n if sub == 0:\n break\n sub = (sub - 1) & rest\n\n results = set()\n\n def dfs(remaining, value):\n if remaining == 0:\n results.add(value)\n return\n for block in choices[remaining]:\n dfs(remaining ^ block, value ^ subset_sum[block])\n\n dfs(size - 1, 0)\n print(len(results))\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.000848, "tokens_in": 704, "tokens_out": 1296, "latency_s": 17.77}] |