| [{"task_id": "mmlu-2843", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] The pH of two lakes is measured. Lake A has a pH of 8.0; Lake B has a pH of 6.0. Which of the following statements is correct about these lakes?\nA) Lake B is alkaline.\nB) Lake B is 100 times more alkaline than Lake A.\nC) The hydrogen ion concentration of Lake B is 104 M.\nD) The pH of both lakes will decrease in response to acid rain.\n\nAnswer with the letter only.", "response": "D", "cost_usd": 4.29e-05, "tokens_in": 111, "tokens_out": 53, "latency_s": 4.997}, {"task_id": "mmlu-568", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Hydrogen ions are formed when:\nA) glycogen becomes depleted.\nB) phosphocreatine breakdown occurs.\nC) pyruvate is converted to lactate.\nD) glycolysis is being used as a major means of resynthesising ATP.\n\nAnswer with the letter only.", "response": "C", "cost_usd": 9.699999999999999e-06, "tokens_in": 67, "tokens_out": 5, "latency_s": 1.478}, {"task_id": "gsm8k-360", "model": "openai/gpt-5.6-luna", "prompt": "Carver just turned 45 years old, which makes him 5 years less than twice the age of his son. How old is his son, in years?\n\nReason step by step, then give the final answer as a single number.", "response": "Let the son\u2019s age be \\(x\\).\n\n\\[\n45 = 2x - 5\n\\]\n\nAdd 5:\n\n\\[\n50 = 2x\n\\]\n\nDivide by 2:\n\n\\[\nx = 25\n\\]\n\n25", "cost_usd": 8.109999999999999e-05, "tokens_in": 55, "tokens_out": 126, "latency_s": 2.739}, {"task_id": "gsm8k-1245", "model": "openai/gpt-5.6-luna", "prompt": "Mary is making ice cubes with fruit frozen in them for a cocktail party. She makes some strawberry cubes, and a number of blueberry cubes equal to 5 times the number of strawberry cubes minus 4. If she makes 116 ice cubes total, how many blueberry cubes does she make?\n\nReason step by step, then give the final answer as a single number.", "response": "Let \\(s\\) be the number of strawberry cubes.\n\nBlueberry cubes: \\(5s - 4\\)\n\nTotal:\n\\[\ns + (5s - 4) = 116\n\\]\n\\[\n6s - 4 = 116\n\\]\n\\[\n6s = 120\n\\]\n\\[\ns = 20\n\\]\n\nBlueberry cubes:\n\\[\n5(20) - 4 = 96\n\\]\n\n\\[\n\\boxed{96}\n\\]", "cost_usd": 0.00010990000000000002, "tokens_in": 79, "tokens_out": 170, "latency_s": 2.914}, {"task_id": "lcb-abc396_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer sequence of length N: A = (A_1,A_2,\\ldots,A_N).\nDetermine whether there is a place in A where the same element appears three or more times in a row.\nMore formally, determine whether there exists an integer i with 1 \\le i \\le N-2 such that A_i = A_{i+1} = A_{i+2}.\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\nIf there is a place in A where the same element appears three or more times in a row, print Yes. Otherwise, print No.\n\nConstraints\n\n\n- 3 \\le N \\le 100\n- 1 \\le A_i \\le 100\n- All input values are integers.\n\nSample Input 1\n\n5\r\n1 4 4 4 2\n\nSample Output 1\n\nYes\r\n\nWe have A=(1,4,4,4,2). There is a place where 4 appears three times in a row, so print Yes.\n\nSample Input 2\n\n6\r\n2 4 4 2 2 4\n\nSample Output 2\n\nNo\r\n\nWe have A=(2,4,4,2,2,4). There is no place where the same element appears three or more times in a row, so print No.\n\nSample Input 3\n\n8\r\n1 4 2 5 7 7 7 2\n\nSample Output 3\n\nYes\n\nSample Input 4\n\n10\r\n1 2 3 4 5 6 7 8 9 10\n\nSample Output 4\n\nNo\n\nSample Input 5\n\n13\r\n1 1 1 1 1 1 1 1 1 1 1 1 1\n\nSample Output 5\n\nYes\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 data = list(map(int, sys.stdin.read().split()))\n n = data[0]\n a = data[1:1 + n]\n\n for i in range(n - 2):\n if a[i] == a[i + 1] == a[i + 2]:\n print(\"Yes\")\n return\n\n print(\"No\")\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.0001002, "tokens_in": 438, "tokens_out": 94, "latency_s": 1.4}, {"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\nsys.setrecursionlimit(100000)\n\ndef main():\n input = sys.stdin.readline\n n = int(input())\n a = list(map(int, input().split()))\n\n groups = []\n results = set()\n\n def dfs(i, current_xor):\n if i == n:\n results.add(current_xor)\n return\n\n x = a[i]\n m = len(groups)\n\n for j in range(m):\n old = groups[j]\n new = old + x\n groups[j] = new\n dfs(i + 1, current_xor ^ old ^ new)\n groups[j] = old\n\n groups.append(x)\n dfs(i + 1, current_xor ^ x)\n groups.pop()\n\n dfs(0, 0)\n print(len(results))\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.0011132, "tokens_in": 704, "tokens_out": 1738, "latency_s": 23.346}] |