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with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{1}{2015}", "style": "rule" }
{ "index": 307, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2304", "style": "rule" }
{ "index": 53, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "4519", "style": "rule" }
{ "index": 404, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "502", "style": "rule" }
{ "index": 323, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "408", "style": "rule" }
{ "index": 414, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "(n-1)(n-2)/2", "style": "rule" }
{ "index": 388, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2\\omega(m) + 1", "style": "rule" }
{ "index": 251, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\min(m, n)^{\\frac{1}{r} - \\frac{1}{s}}", "style": "rule" }
{ "index": 5, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "-26", "style": "rule" }
{ "index": 365, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "Yes", "style": "rule" }
{ "index": 80, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "63", "style": "rule" }
{ "index": 181, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "5.1", "style": "rule" }
{ "index": 112, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{5}{2} \\sqrt{409}", "style": "rule" }
{ "index": 102, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "864", "style": "rule" }
{ "index": 163, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\arcsin \\frac{1}{\\sqrt{3}}", "style": "rule" }
{ "index": 328, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2852", "style": "rule" }
{ "index": 171, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{\\sqrt{3}}{3}, 1, \\frac{3 \\sqrt{3}}{5}", "style": "rule" }
{ "index": 137, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "Yes", "style": "rule" }
{ "index": 170, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{375}{8}", "style": "rule" }
{ "index": 386, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "284688", "style": "rule" }
{ "index": 303, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "The possible values of \\( f(1000) \\) are all even numbers.", "style": "rule" }
{ "index": 351, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{1}{4}", "style": "rule" }
{ "index": 394, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "29", "style": "rule" }
{ "index": 191, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "30212", "style": "rule" }
{ "index": 373, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "4 p(p-1)", "style": "rule" }
{ "index": 366, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "96", "style": "rule" }
{ "index": 357, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "0", "style": "rule" }
{ "index": 364, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{187465}{6744582}", "style": "rule" }
{ "index": 296, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "252", "style": "rule" }
{ "index": 111, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "20", "style": "rule" }
{ "index": 173, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "30", "style": "rule" }
{ "index": 259, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "49", "style": "rule" }
{ "index": 313, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "16", "style": "rule" }
{ "index": 305, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "The probability that $C$ is a polygon with four vertices is larger than the probability that $C$ is a polygon with three vertices.", "style": "rule" }
{ "index": 195, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2", "style": "rule" }
{ "index": 263, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\binom{n}{2} + 1", "style": "rule" }
{ "index": 422, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "32", "style": "rule" }
{ "index": 158, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "1217", "style": "rule" }
{ "index": 385, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{3 \\pi}{4}", "style": "rule" }
{ "index": 398, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "$n = k + 4$", "style": "rule" }
{ "index": 338, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\[\n\\frac{1}{3}\n\\]", "style": "rule" }
{ "index": 197, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "$\\frac{4}{5}$", "style": "rule" }
{ "index": 119, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2016", "style": "rule" }
{ "index": 315, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "(n + 1)! - (n - 1)!", "style": "rule" }
{ "index": 253, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "The values of $n$ are $2^{2^1}$, $2^{2^2}$, $2^{2^4}$, $2^{2^8}$.", "style": "rule" }
{ "index": 188, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\lfloor n / 2\\rfloor+1", "style": "rule" }
{ "index": 278, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\pi / e", "style": "rule" }
{ "index": 15, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "16", "style": "rule" }
{ "index": 274, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "4", "style": "rule" }
{ "index": 392, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "n", "style": "rule" }
{ "index": 424, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "274", "style": "rule" }
{ "index": 410, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "x = (3^{1/5}+1)/2, y = (3^{1/5}-1)/2", "style": "rule" }
{ "index": 193, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "512", "style": "rule" }
{ "index": 236, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{2}{3}", "style": "rule" }
{ "index": 47, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "12", "style": "rule" }
{ "index": 260, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "28", "style": "rule" }
{ "index": 182, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "2(n! + 1)", "style": "rule" }
{ "index": 329, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "80", "style": "rule" }
{ "index": 176, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\frac{1}{512}", "style": "rule" }
{ "index": 369, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "23097", "style": "rule" }
{ "index": 198, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "1344", "style": "rule" }
{ "index": 330, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "\\binom{n}{2} - (n - 2)", "style": "rule" }
{ "index": 324, "split": "with-guidance" }
easy-with-guidance
with-guidance
[ { "content": "You are given a problem and a partial solution.\n\nYour task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correc...
math
{ "ground_truth": "201", "style": "rule" }
{ "index": 75, "split": "with-guidance" }
easy-with-guidance
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