ultraviolet
Collection
3 items • Updated
Datasets:
problem_id stringlengths 9 39 | source stringclasses 15
values | slice stringclasses 1
value | teacher stringclasses 1
value | origin stringclasses 1
value | problem stringlengths 17 1.47k | trace stringlengths 149 17.6k | thinking stringlengths 109 17.6k | solution stringlengths 9 133 | answer stringlengths 1 125 | answer_teacher stringlengths 1 110 | ref_raw stringlengths 1 125 | n_tokens int64 82 4.1k | level_llm null | gold_level stringclasses 5
values | bm_solve_rate float64 0 1 ⌀ | teacher_solve_rate float64 0.25 1 | k int64 4 4 | n_usable int64 1 4 | raw_tag stringclasses 44
values | raw_j int64 0 3 | in_mathcont bool 2
classes | in_anyans bool 2
classes | in_midv31 stringclasses 2
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
n15-train-00000-18560 | numina15:olympiads | S6 | violetto | gen | 5.1. In a row, there are 27 matchboxes, each containing a certain number of matches. It is known that in any four consecutive boxes, the total is 25 matches, and in all of them, the total is 165. How many matches are in the eighth box? | <think>
We need to parse the problem: "In a row, there are 27 matchboxes, each containing a certain number of matches. It is known that in any four consecutive boxes, the total is 25 matches, and in all of them, the total is 165. How many matches are in the eighth box? Please reason step by step, and put your final ans... | We need to parse the problem: "In a row, there are 27 matchboxes, each containing a certain number of matches. It is known that in any four consecutive boxes, the total is 25 matches, and in all of them, the total is 165. How many matches are in the eighth box? Please reason step by step, and put your final answer with... | \boxed{10} | 10 | 10 | 10 | 3,838 | null | null | null | 1 | 4 | 1 | pilot-0 | 0 | true | true | null |
n15-train-00001-135706 | numina15:cn_k12 | S6 | violetto | gen | A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? | <think>
We need to parse the problem: "A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? Please reason step by step, and put your final answer within \boxed{}."
We have a gro... | We need to parse the problem: "A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? Please reason step by step, and put your final answer within \boxed{}."
We have a group with ... | \boxed{\frac{2}{3}} | \frac{2}{3} | \frac{2}{3} | \frac{2}{3} | 483 | null | null | null | 1 | 4 | 4 | pilot-1 | 0 | true | true | S1 |
n15-train-00001-135706 | numina15:cn_k12 | S6 | violetto | gen | A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? | <think>
We need to parse the problem: "A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? Please reason step by step, and put your final answer within \boxed{}."
We need to co... | We need to parse the problem: "A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? Please reason step by step, and put your final answer within \boxed{}."
We need to compute pr... | \boxed{\frac{2}{3}} | \frac{2}{3} | \frac{2}{3} | \frac{2}{3} | 455 | null | null | null | 1 | 4 | 4 | pilot-1 | 1 | true | true | S1 |
n15-train-00001-135706 | numina15:cn_k12 | S6 | violetto | gen | A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? | <think>
We need to solve a probability problem: A hobby group has 2 boys and 1 girl. Total 3 students. Randomly select 2 students (without replacement). Find probability that exactly one boy and one girl are chosen.
We need to reason step by step, then final answer in \boxed{}.
We need to be careful: The sample space... | We need to solve a probability problem: A hobby group has 2 boys and 1 girl. Total 3 students. Randomly select 2 students (without replacement). Find probability that exactly one boy and one girl are chosen.
We need to reason step by step, then final answer in \boxed{}.
We need to be careful: The sample space: number... | \boxed{\frac{2}{3}} | \frac{2}{3} | \frac{2}{3} | \frac{2}{3} | 412 | null | null | null | 1 | 4 | 4 | pilot-1 | 2 | true | true | S1 |
n15-train-00001-135706 | numina15:cn_k12 | S6 | violetto | gen | A hobby group consists of 2 boys and 1 girl. If two students are randomly selected to participate in a questionnaire survey, what is the probability that exactly one boy and one girl are chosen? | <think>
We need to answer a probability question: A hobby group consists of 2 boys and 1 girl. Total students = 3. Choose 2 randomly (without order, uniformly among all 2-element subsets). We need probability that exactly one boy and one girl are chosen.
We can compute: total number of ways to choose any 2 from 3: C(3... | We need to answer a probability question: A hobby group consists of 2 boys and 1 girl. Total students = 3. Choose 2 randomly (without order, uniformly among all 2-element subsets). We need probability that exactly one boy and one girl are chosen.
We can compute: total number of ways to choose any 2 from 3: C(3,2)=3. F... | \boxed{\frac{2}{3}} | \frac{2}{3} | \frac{2}{3} | \frac{2}{3} | 570 | null | null | null | 1 | 4 | 4 | pilot-1 | 3 | true | true | S1 |
n15-train-00001-142118 | numina15:cn_k12 | S6 | violetto | gen | Given the ellipse $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{12} = 1$ and its right focus $F$, if the distance from $F$ to the asymptote of the hyperbola $E$: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$ $(a > 0, b > 0)$ is less than $\sqrt{3}$, then the range of the eccentricity $e$ of the hyperbola $E$ is ______. | <think>
We need to parse the problem: There's an ellipse given by x^2/16 + y^2/12 = 1. Its right focus is F. There's a hyperbola E: x^2/a^2 - y^2/b^2 = 1, with a>0, b>0. The distance from F to the asymptote of the hyperbola E is less than sqrt(3). We need to find the range of the eccentricity e of the hyperbola E that ... | We need to parse the problem: There's an ellipse given by x^2/16 + y^2/12 = 1. Its right focus is F. There's a hyperbola E: x^2/a^2 - y^2/b^2 = 1, with a>0, b>0. The distance from F to the asymptote of the hyperbola E is less than sqrt(3). We need to find the range of the eccentricity e of the hyperbola E that satisfie... | \boxed{1 < e < 2} | 1 < e < 2 | 1<e<2 | 1 < e < 2 | 3,114 | null | null | null | 0.75 | 4 | 1 | pilot-6 | 2 | false | true | null |
n15-train-00001-178935 | numina15:cn_k12 | S6 | violetto | gen | In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A or C. How many different arran... | <think>
We need to parse the problem carefully. It says: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can... | We need to parse the problem carefully. It says: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be... | \boxed{36} | 36 | 36 | 36 | 3,821 | null | null | null | 1 | 4 | 4 | pilot-8 | 0 | true | true | S1 |
n15-train-00001-178935 | numina15:cn_k12 | S6 | violetto | gen | In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A or C. How many different arran... | <think>
We need to parse the problem: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by ... | We need to parse the problem: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A... | \boxed{36} | 36 | 36 | 36 | 3,709 | null | null | null | 1 | 4 | 4 | pilot-8 | 1 | true | true | S1 |
n15-train-00001-178935 | numina15:cn_k12 | S6 | violetto | gen | In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A or C. How many different arran... | <think>
We need to parse the problem: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by ... | We need to parse the problem: "In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A... | \boxed{36} | 36 | 36 | 36 | 2,082 | null | null | null | 1 | 4 | 4 | pilot-8 | 2 | true | true | S1 |
n15-train-00001-178935 | numina15:cn_k12 | S6 | violetto | gen | In one morning, a class has 4 lessons, and each lesson needs one teacher to teach it. There are 6 teachers, named A, B, C, D, E, and F, to arrange 4 of them to teach one lesson each. The first lesson can only be taught by either A or B, and the fourth lesson can only be taught by either A or C. How many different arran... | <think>
We need to parse the problem carefully. There are 6 teachers: A, B, C, D, E, F. There are 4 lessons (presumably distinct, ordered: lesson 1, 2, 3, 4). Each lesson needs one teacher to teach it. We have 6 teachers available, but we need to assign a teacher to each of the 4 distinct lessons, with the constraints:... | We need to parse the problem carefully. There are 6 teachers: A, B, C, D, E, F. There are 4 lessons (presumably distinct, ordered: lesson 1, 2, 3, 4). Each lesson needs one teacher to teach it. We have 6 teachers available, but we need to assign a teacher to each of the 4 distinct lessons, with the constraints: lesson ... | \boxed{36} | 36 | 36 | 36 | 4,037 | null | null | null | 1 | 4 | 4 | pilot-8 | 3 | true | true | S1 |
n15-train-00000-154276 | numina15:olympiads | S6 | violetto | gen | 6. Rationalize the denominator of $\frac{6}{\sqrt[3]{4}+\sqrt[3]{16}+\sqrt[3]{64}}$ and simplify. | <think>
We need to rationalize denominator of expression: 6 / (cuberoot(4) + cuberoot(16) + cuberoot(64)). Simplify. Let's denote cube roots: ∛4, ∛16, ∛64. Note ∛64 = 4 (since 4^3 = 64). ∛4 = 4^{1/3}. ∛16 = 16^{1/3} = (2^4)^{1/3} = 2^{4/3} = 2 * 2^{1/3} = 2∛2. ∛4 = (2^2)^{1/3} = 2^{2/3} = (∛2)^2. Let's set x = ∛2. Then... | We need to rationalize denominator of expression: 6 / (cuberoot(4) + cuberoot(16) + cuberoot(64)). Simplify. Let's denote cube roots: ∛4, ∛16, ∛64. Note ∛64 = 4 (since 4^3 = 64). ∛4 = 4^{1/3}. ∛16 = 16^{1/3} = (2^4)^{1/3} = 2^{4/3} = 2 * 2^{1/3} = 2∛2. ∛4 = (2^2)^{1/3} = 2^{2/3} = (∛2)^2. Let's set x = ∛2. Then x^3 = 2... | \boxed{2-\sqrt[3]{2}} | 2-\sqrt[3]{2} | 2-\sqrt[3]{2} | 2-\sqrt[3]{2} | 3,927 | null | null | null | 0.75 | 4 | 1 | pilot-13 | 3 | false | true | null |
bm-239702 | bigmath:big_math | S6 | violetto | gen | Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. | <think>
We have a user asking a simple arithmetic problem: Given x=2 and y=1, calculate 2x - 3y. Need to reason step by step, and final answer within \boxed{}. Straightforward.
Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Then 2x - 3y = 4 - 3 = 1. So answer is 1. Put in \boxed{1}.
Need to provide step-by-step reasonin... | We have a user asking a simple arithmetic problem: Given x=2 and y=1, calculate 2x - 3y. Need to reason step by step, and final answer within \boxed{}. Straightforward.
Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Then 2x - 3y = 4 - 3 = 1. So answer is 1. Put in \boxed{1}.
Need to provide step-by-step reasoning. Ensur... | \boxed{1} | 1 | 1 | 1 | 216 | null | null | 0.984375 | 1 | 4 | 4 | pilot-15 | 0 | true | true | null |
bm-239702 | bigmath:big_math | S6 | violetto | gen | Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. | <think>
We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
We need to compute 2x - 3y with x=2, y=1.
2x = 2*2 = 4. 3y = 3*1 = 3. 4 - 3 = 1. So answer ... | We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
We need to compute 2x - 3y with x=2, y=1.
2x = 2*2 = 4. 3y = 3*1 = 3. 4 - 3 = 1. So answer is 1.
W... | \boxed{1} | 1 | 1 | 1 | 230 | null | null | 0.984375 | 1 | 4 | 4 | pilot-15 | 1 | true | true | null |
bm-239702 | bigmath:big_math | S6 | violetto | gen | Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. | <think>
We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
This is straightforward arithmetic. x=2, y=1. Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Th... | We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
This is straightforward arithmetic. x=2, y=1. Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Then 2x - ... | \boxed{1} | 1 | 1 | 1 | 268 | null | null | 0.984375 | 1 | 4 | 4 | pilot-15 | 2 | true | true | null |
bm-239702 | bigmath:big_math | S6 | violetto | gen | Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. | <think>
We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
This is straightforward arithmetic. x=2, y=1. Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Th... | We need to parse the problem: "Given that x = 2 and y = 1, calculate the value of the expression 2x - 3y. Express your answer as a single integer. Please reason step by step, and put your final answer within \boxed{}."
This is straightforward arithmetic. x=2, y=1. Compute 2x = 2*2 = 4. Compute 3y = 3*1 = 3. Then 2x - ... | \boxed{1} | 1 | 1 | 1 | 276 | null | null | 0.984375 | 1 | 4 | 4 | pilot-15 | 3 | true | true | null |
n15-train-00000-89377 | numina15:olympiads | S6 | violetto | gen | Task A-2.1. (8 points)
Simplify the fraction $\frac{\left(2^{n-1}+1\right)^{2}-4^{n-1}}{4^{n}+2^{n+1}+1}$. | <think>
We need to simplify the fraction:
\[
\frac{(2^{n-1}+1)^2 - 4^{n-1}}{4^n + 2^{n+1} + 1}
\]
We need to simplify algebraically, presumably in terms of n, maybe cancel factors. Let's do step-by-step.
Given expression:
Numerator: (2^{n-1}+1)^2 - 4^{n-1}.
Denominator: 4^n + 2^{n+1} + 1.
We can rewrite everythin... | We need to simplify the fraction:
\[
\frac{(2^{n-1}+1)^2 - 4^{n-1}}{4^n + 2^{n+1} + 1}
\]
We need to simplify algebraically, presumably in terms of n, maybe cancel factors. Let's do step-by-step.
Given expression:
Numerator: (2^{n-1}+1)^2 - 4^{n-1}.
Denominator: 4^n + 2^{n+1} + 1.
We can rewrite everything in ter... | \boxed{\frac{1}{2^{n}+1}} | \frac{1}{2^{n}+1} | \frac{1}{2^n+1} | \frac{1}{2^{n}+1} | 1,675 | null | null | null | 1 | 4 | 4 | pilot-16 | 0 | false | true | null |
End of preview. Expand in Data Studio
violetto-math-traces
Math reasoning traces generated by paradigma-inc/limite-1b-violetto
(T = 0.6, top-p 0.95). Each trace is <think>...</think> followed by a short solution ending in \boxed{}. Every
kept trace's final answer is correct. Problems come from NuminaMath-1.5, Big-Math and the MATH training set.
| config / split | rows | contents |
|---|---|---|
| mid-alpha / train | 387,395 | SFT file of ultraviolet-50m-mid-alpha: Violetto traces plus synthetic arithmetic / procedure text, 2 epochs (field block) |
| mid-alpha / validation | 2,216 | held-out rows (problems not in train) |
| broad / train | 41,007 | traces on a broader and harder problem pool |
provenance/mid-alpha-trace-rows.jsonl gives the source problem id of every Violetto row in mid-alpha.
Usage
from datasets import load_dataset
ds = load_dataset("harribo11/violetto-math-traces", "mid-alpha", split="train")
To train on it: scripts/sft_blocks.py in github.com/hliuson/ultraviolet.
License
Apache-2.0 (the generating model's license). The problems keep their source datasets' terms.
- Downloads last month
- 29