id stringlengths 23 23 | source stringclasses 1
value | domain stringclasses 1
value | task_type stringclasses 1
value | mode stringclasses 1
value | lang stringclasses 1
value | tools stringclasses 1
value | messages stringlengths 745 63.3k | metadata stringlengths 516 525 |
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NuminaMath-CoT_00000027 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Given the function \\( f(x) = 2x + 4 \\), find the increment of any of its antiderivatives as \\( x \\) changes from -2 to 0.", "role": "user"}, {"content": "To find the increment of any antiderivative of $f(x) = 2x + 4$ as $x$ changes from $-2$ to $0$, we need to calculate the change in the value of the ... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 216, "num_input_tokens": 1092, "num_loss_tokens": 981, "num_reasoning_tokens": 765, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000027", "quality_score": null, "reasoning_assistant_turns": 1, "reasoni... |
NuminaMath-CoT_00000030 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "A circle with radius \\(R\\) passes through the vertex \\(A\\) of an isosceles triangle \\(ABC\\), is tangent to the base \\(BC\\) at point \\(B\\), and intersects the lateral side \\(AC\\) at point \\(D\\). Find the lateral side \\(AB\\), given that \\(\\frac{AD}{DX} = k\\).", "role": "user"}, {"content"... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 808, "num_input_tokens": 14586, "num_loss_tokens": 13559, "num_reasoning_tokens": 12751, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000030", "quality_score": null, "reasoning_assistant_turns": 1, "re... |
NuminaMath-CoT_00000019 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Denote by \\( d(n) \\) the number of positive divisors of a positive integer \\( n \\). Prove that there are infinitely many positive integers \\( n \\) such that \\( |\\sqrt{3} \\cdot d(n)| \\) divides \\( n \\).", "role": "user"}, {"content": "To prove that there are infinitely many positive integers \\... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 387, "num_input_tokens": 9117, "num_loss_tokens": 8741, "num_reasoning_tokens": 8354, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000019", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000021 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "In the convex quadrilateral FIDO, the opposite sides FI and DO are equal to each other and are longer than side DI. It is known that ∠FIO = ∠DIO. Prove that FO is longer than DI.", "role": "user"}, {"content": "To prove that $FO > DI$ in the convex quadrilateral $FIDO$, we will use the Law of Cosines on t... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 7, "num_input_tokens": 7185, "num_loss_tokens": 6659, "num_reasoning_tokens": 6652, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000021", "quality_score": null, "reasoning_assistant_turns": 1, "reasoni... |
NuminaMath-CoT_00000024 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Calculate the limit of the function:\n\n$$\\lim_{x \\rightarrow 0} \\frac{\\operatorname{tg} x - \\sin x}{x(1 - \\cos 2x)}$$", "role": "user"}, {"content": "To calculate the limit:\n$$ L = \\lim_{x \\rightarrow 0} \\frac{\\tan x - \\sin x}{x(1 - \\cos 2x)} $$\n\nWe can solve this using Taylor series expan... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 45, "num_input_tokens": 3085, "num_loss_tokens": 2850, "num_reasoning_tokens": 2805, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000024", "quality_score": null, "reasoning_assistant_turns": 1, "reason... |
NuminaMath-CoT_00000041 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Misha, during the summer at the dacha, made a homemade darts. The circular board is divided by circles into several sectors for throwing darts. Points are awarded according to the number written in the sector, as shown in the picture.\n\nMisha threw 8 darts three times. The second time he scored 2 times m... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 6, "num_input_tokens": 5831, "num_loss_tokens": 5575, "num_reasoning_tokens": 5569, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000041", "quality_score": null, "reasoning_assistant_turns": 1, "reasoni... |
NuminaMath-CoT_00000044 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Mrs. Toad has a class of 2017 students, with unhappiness levels \\(1, 2, \\ldots, 2017\\) respectively. Today in class, there is a group project and Mrs. Toad wants to split the class into exactly 15 groups. The unhappiness level of a group is the average unhappiness of its members, and the unhappiness of... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 700, "num_input_tokens": 7659, "num_loss_tokens": 7213, "num_reasoning_tokens": 6513, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000044", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000046 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "The common difference of an increasing arithmetic progression, consisting of natural numbers, is a natural number ending in 2019. Can three consecutive terms of this progression be squares of natural numbers?", "role": "user"}, {"content": "No, three consecutive terms of this arithmetic progression cannot... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 546, "num_input_tokens": 3376, "num_loss_tokens": 3143, "num_reasoning_tokens": 2597, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000046", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000034 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "In chess tournaments, each victory is worth 1 point, each draw is worth 0.5 points, and each loss is worth zero points. In the \"Magistral Championship\" of chess, only International Masters (IMs) and Grand Masters (GMs) participated. The number of GMs was ten times the number of IMs. Each player played o... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 538, "num_input_tokens": 4628, "num_loss_tokens": 4225, "num_reasoning_tokens": 3687, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000034", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000057 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Let \\( d_n \\) be the last nonzero digit of the decimal representation of \\( n! \\). Prove that \\( d_n \\) is aperiodic; that is, there do not exist \\( T \\) and \\( n_0 \\) such that for all \\( n \\geq n_0 \\), \\( d_{n+T} = d_n \\).", "role": "user"}, {"content": "The last nonzero digit of \\( n! \... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 629, "num_input_tokens": 12722, "num_loss_tokens": 12083, "num_reasoning_tokens": 11454, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000057", "quality_score": null, "reasoning_assistant_turns": 1, "re... |
NuminaMath-CoT_00000059 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Given that the sequence $\\left\\{a_{n}\\right\\}$ is a geometric sequence with the first term of 1 and a common ratio of 2, and the sequence $\\left\\{b_{n}\\right\\}$ is an arithmetic sequence with the first term of 2 and a common difference of 5, find the 100th term, $x_{100}$, of the sequence $\\left\... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 358, "num_input_tokens": 3359, "num_loss_tokens": 3123, "num_reasoning_tokens": 2765, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000059", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000064 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Let $[E F]$ be a segment contained within the segment $[B C]$ such that the semicircle with diameter $[E F]$ is tangent to $[A B]$ at $Q$ and to $[A C]$ at $P$.\n\nProve that the intersection point $K$ of the lines $(E P)$ and $(F Q)$ lies on the altitude from $A$ in triangle $A B C$.", "role": "user"}, {... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 469, "num_input_tokens": 15655, "num_loss_tokens": 14394, "num_reasoning_tokens": 13925, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000064", "quality_score": null, "reasoning_assistant_turns": 1, "re... |
NuminaMath-CoT_00000075 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "In triangle \\( \\triangle ABC \\), \\( BC = a \\), \\( CA = b \\), and \\( AB = c \\). If \\( b \\) is the geometric mean of \\( a \\) and \\( c \\), and \\( \\sin A \\) is the arithmetic mean of \\( \\sin (B - A) \\) and \\( \\sin C \\), find the value of \\( \\cos B \\).", "role": "user"}, {"content": ... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 886, "num_input_tokens": 4185, "num_loss_tokens": 3691, "num_reasoning_tokens": 2805, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000075", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000077 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Point \\( F \\) is the midpoint of side \\( BC \\) of square \\( ABCD \\). A perpendicular \\( AE \\) is drawn to segment \\( DF \\). Find the angle \\( CEF \\).", "role": "user"}, {"content": "To find the angle $\\angle CEF$, we can use coordinate geometry. Let's place the square $ABCD$ in the Cartesian ... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 523, "num_input_tokens": 4107, "num_loss_tokens": 3836, "num_reasoning_tokens": 3313, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000077", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000086 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "\\( P \\) is a point inside triangle \\(ABC\\), and lines \\(AP\\), \\(BP\\), \\(CP\\) intersect the opposite sides \\(BC\\), \\(CA\\), \\(AB\\) in points \\(D\\), \\(E\\), \\(F\\), respectively. It is given that \\(\\angle APB = 90^\\circ\\), and that \\(AC = BC\\) and \\(AB = BD\\). We also know that \\... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 628, "num_input_tokens": 11811, "num_loss_tokens": 10830, "num_reasoning_tokens": 10202, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000086", "quality_score": null, "reasoning_assistant_turns": 1, "re... |
NuminaMath-CoT_00000102 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Alyosha cut a cube of size \\( n \\times n \\times n \\) into 153 smaller cubes. In this process, all but one of the smaller cubes have an edge length of 1. Find \\( n \\).", "role": "user"}, {"content": "The problem states that a cube of size $n \\times n \\times n$ is cut into 153 smaller cubes, where 1... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 472, "num_input_tokens": 2238, "num_loss_tokens": 2028, "num_reasoning_tokens": 1556, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000102", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000120 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Three tired cowboys entered a saloon and hung their hats on a bison horn at the entrance. Late at night, when the cowboys were leaving, they were unable to distinguish one hat from another and randomly took three hats. Find the probability that none of them took their own hat.", "role": "user"}, {"content... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 70, "num_input_tokens": 1696, "num_loss_tokens": 1568, "num_reasoning_tokens": 1498, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000120", "quality_score": null, "reasoning_assistant_turns": 1, "reason... |
NuminaMath-CoT_00000130 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "An 8 by 8 grid of numbers follows this pattern:\n1) The first row and first column consist of all 1s.\n2) The entry in the \\(i\\)th row and \\(j\\)th column equals the sum of the numbers in the \\((i-1)\\) by \\((j-1)\\) sub-grid with row less than \\(i\\) and column less than \\(j\\).\n\nWhat is the num... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 8, "num_input_tokens": 16622, "num_loss_tokens": 15515, "num_reasoning_tokens": 15507, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000130", "quality_score": null, "reasoning_assistant_turns": 1, "reas... |
NuminaMath-CoT_00000134 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Write a cone around a sphere with radius $r$ such that the volume of the cone is minimized. What is the volume of this cone?", "role": "user"}, {"content": "To find the volume of the cone with the minimum volume that can be circumscribed around a sphere of radius $r$, we proceed with the following steps:\... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 580, "num_input_tokens": 3421, "num_loss_tokens": 3181, "num_reasoning_tokens": 2601, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000134", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000140 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "Let the set \\( M = \\{1, 2, \\cdots, 1000\\} \\). For any non-empty subset \\( X \\) of \\( M \\), let \\( a_X \\) represent the sum of the maximum and minimum numbers in \\( X \\). What is the arithmetic mean of all such \\( a_X \\)?", "role": "user"}, {"content": "To find the arithmetic mean of $a_X = ... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 594, "num_input_tokens": 5504, "num_loss_tokens": 5132, "num_reasoning_tokens": 4538, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000140", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
NuminaMath-CoT_00000141 | NuminaMath-CoT | math | reasoning | reasoning | en | [] | [{"content": "The center of the hyperbola is at the origin \\( O \\), with its foci on the \\( x \\)-axis. A line passing through the right focus of the hyperbola with a slope of \\( \\sqrt{\\frac{3}{5}} \\) intersects the hyperbola at points \\( P \\) and \\( Q \\). If \\( P O \\perp O Q \\) and \\(|P Q| = 4\\), find ... | {"contaminated": false, "contamination_matches": [], "license": "CC-BY-4.0", "num_final_answer_tokens": 703, "num_input_tokens": 6034, "num_loss_tokens": 5536, "num_reasoning_tokens": 4833, "num_tool_call_tokens": 0, "original_id": "NuminaMath-CoT_00000141", "quality_score": null, "reasoning_assistant_turns": 1, "reaso... |
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