Datasets:
task_id stringlengths 26 34 | input stringlengths 189 1.32k | raw_output stringlengths 3.16k 110k | thinking_content stringlengths 2.35k 107k ⌀ | final_answer stringlengths 537 110k | finish_reason stringclasses 2
values | prompt_tokens int64 56 650 | completion_tokens int64 959 32.8k | temperature float64 0 0 | max_tokens int64 32.8k 32.8k |
|---|---|---|---|---|---|---|---|---|---|
AMC_12__2012_AMC_12A_Problems__p21 | Let $a$, $b$, and $c$ be positive integers with $a\ge$ $b\ge$ $c$ such that
$a^2-b^2-c^2+ab=2011$ and
$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.
What is $a$?
$\textbf{(A)}\ 249\qquad\textbf{(B)}\ 250\qquad\textbf{(C)}\ 251\qquad\textbf{(D)}\ 252\qquad\textbf{(E)}\ 253$
Please reason step by step, and put your final answer wit... | <think>
Okay, so I need to solve this problem where I have two equations involving a, b, and c, which are positive integers with a ≥ b ≥ c. The equations are:
1. $ a^2 - b^2 - c^2 + ab = 2011 $
2. $ a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc = -1997 $
And I need to find the value of a, with the options given from 249 to 253... |
Okay, so I need to solve this problem where I have two equations involving a, b, and c, which are positive integers with a ≥ b ≥ c. The equations are:
1. $ a^2 - b^2 - c^2 + ab = 2011 $
2. $ a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc = -1997 $
And I need to find the value of a, with the options given from 249 to 253. Alrig... | We are given two equations involving positive integers $ a, b, c $ with the condition $ a \ge b \ge c $:
1. $ a^2 - b^2 - c^2 + ab = 2011 $
2. $ a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc = -1997 $
---
### Step 1: Combine the Equations
Add both equations:
$$
(a^2 - b^2 - c^2 + ab) + (a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc) ... | stop | 178 | 5,839 | 0 | 32,768 |
AMC_10__2014_AMC_10A_Problems__p3 | Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for $\textdollar 2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf co... | <think>
Okay, so Bridget bakes 48 loaves of bread. Let me try to figure out her profit for the day. Profit is total revenue minus total cost, right? So I need to calculate how much money she makes from selling the loaves in the morning, afternoon, and late afternoon, then subtract the cost of making all those loaves.
... | null | <think>
Okay, so Bridget bakes 48 loaves of bread. Let me try to figure out her profit for the day. Profit is total revenue minus total cost, right? So I need to calculate how much money she makes from selling the loaves in the morning, afternoon, and late afternoon, then subtract the cost of making all those loaves.
... | length | 195 | 32,768 | 0 | 32,768 |
AMC_12__2018_AMC_12A_Problems__p6 | For positive integers $m$ and $n$ such that $m+10<n+1$, both the mean and the median of the set $\{m, m+4, m+10, n+1, n+2, 2n\}$ are equal to $n$. What is $m+n$?
$\textbf{(A)}20\qquad\textbf{(B)}21\qquad\textbf{(C)}22\qquad\textbf{(D)}23\qquad\textbf{(E)}24$
Please reason step by step, and put your final answer within... | <think>
Okay, so I need to solve this problem where I have two positive integers, m and n, with the condition that m + 10 < n + 1. The set given is {m, m + 4, m + 10, n + 1, n + 2, 2n}, and both the mean and the median of this set are equal to n. I need to find m + n. The answer choices are from 20 to 24. Let me try to... |
Okay, so I need to solve this problem where I have two positive integers, m and n, with the condition that m + 10 < n + 1. The set given is {m, m + 4, m + 10, n + 1, n + 2, 2n}, and both the mean and the median of this set are equal to n. I need to find m + n. The answer choices are from 20 to 24. Let me try to work t... | To solve the problem, we are given a set of six numbers:
$$
\{m, m+4, m+10, n+1, n+2, 2n\}
$$
with the conditions:
- $ m + 10 < n + 1 $, which simplifies to $ m < n - 9 $
- The **mean** of the set is $ n $
- The **median** of the set is also $ n $
We are to find the value of $ m + n $.
---
### Step 1: Use the Mea... | stop | 147 | 4,222 | 0 | 32,768 |
USAMO__2019_USAMO_Problems__p4 | "Let $n$ be a nonnegative integer. Determine the number of ways that one can choose $(n+1)^2$ sets $(...TRUNCATED) | "<think>\nOkay, so I need to figure out the number of ways to choose (n+1)^2 sets S_{i,j} that satis(...TRUNCATED) | "\nOkay, so I need to figure out the number of ways to choose (n+1)^2 sets S_{i,j} that satisfy two (...TRUNCATED) | "To determine the number of ways to choose $(n+1)^2$ sets $S_{i,j} \\subseteq \\{1, 2, \\ldots, 2n\\(...TRUNCATED) | stop | 177 | 24,273 | 0 | 32,768 |
AMC_8__1996_AJHSME_Problems__p25 | "A point is chosen at random from within a circular region. What is the probability that the point (...TRUNCATED) | "<think>\nOkay, so I need to find the probability that a randomly chosen point inside a circular reg(...TRUNCATED) | "\nOkay, so I need to find the probability that a randomly chosen point inside a circular region is (...TRUNCATED) | "To determine the probability that a randomly chosen point within a circular region is closer to the(...TRUNCATED) | stop | 136 | 4,009 | 0 | 32,768 |
AIME__2004_AIME_II_Problems__p3 | "A solid rectangular block is formed by gluing together $N$ congruent 1-cm cubes face to face. When (...TRUNCATED) | "<think>\nOkay, so I need to find the smallest possible value of N, where N is the number of 1-cm cu(...TRUNCATED) | "\nOkay, so I need to find the smallest possible value of N, where N is the number of 1-cm cubes in (...TRUNCATED) | "To solve the problem, we are given a solid rectangular block made of $ N $ congruent 1-cm cubes, an(...TRUNCATED) | stop | 90 | 8,619 | 0 | 32,768 |
AHSME__1979_AHSME_Problems__p8 | "Find the area of the smallest region bounded by the graphs of $y=|x|$ and $x^2+y^2=4$.\n$\\textbf{((...TRUNCATED) | "<think>\nOkay, so I need to find the area of the smallest region bounded by the graphs of y = |x| a(...TRUNCATED) | "\nOkay, so I need to find the area of the smallest region bounded by the graphs of y = |x| and x² (...TRUNCATED) | "To find the **smallest region bounded by the graphs** of $ y = |x| $ and $ x^2 + y^2 = 4 $, we begi(...TRUNCATED) | stop | 126 | 15,443 | 0 | 32,768 |
AMC_10__2002_AMC_10A_Problems__p2 | "Given that a, b, and c are non-zero real numbers, define $(a, b, c) = \\frac{a}{b} + \\frac{b}{c} +(...TRUNCATED) | "<think>\nOkay, so I need to find the value of this function defined as (a, b, c) equals a/b plus b/(...TRUNCATED) | "\nOkay, so I need to find the value of this function defined as (a, b, c) equals a/b plus b/c plus (...TRUNCATED) | "To solve the problem, we are given a function defined as:\n\n$$\n(a, b, c) = \\frac{a}{b} + \\frac{(...TRUNCATED) | stop | 142 | 1,622 | 0 | 32,768 |
AMC_10__2005_AMC_10A_Problems__p11 | "A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cube(...TRUNCATED) | "<think>\nOkay, so I need to solve this problem about a wooden cube that's painted red and then cut (...TRUNCATED) | "\nOkay, so I need to solve this problem about a wooden cube that's painted red and then cut into sm(...TRUNCATED) | "To solve the problem, we analyze the relationship between the total number of red faces and the tot(...TRUNCATED) | stop | 135 | 3,263 | 0 | 32,768 |
AHSME__1960_AHSME_Problems__p15 | "Triangle $I$ is equilateral with side $A$, perimeter $P$, area $K$, and circumradius $R$ (radius of(...TRUNCATED) | "<think>\nOkay, so I need to figure out the relationships between the perimeters, areas, and circumr(...TRUNCATED) | "\nOkay, so I need to figure out the relationships between the perimeters, areas, and circumradii of(...TRUNCATED) | "To solve this problem, we analyze the relationships between the perimeters, areas, and circumradii (...TRUNCATED) | stop | 223 | 4,478 | 0 | 32,768 |
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Qwen/Qwen3-32B — creativemath-with-answers
Model outputs from the micro-creativity inference suite.
- Model:
Qwen/Qwen3-32B - Dataset:
creativemath-with-answers(188 items) - Part of collection: ZachW/llm-creativity-benchmarks
Generation config
temperature: 0.0
max_tokens: 32768
seed: 42
backend: vllm
Columns
| Column | Description |
|---|---|
task_id |
Unique task identifier |
input |
The exact prompt sent to the model (after meta-prompt application) |
raw_output |
Full model output string |
thinking_content |
Extracted chain-of-thought / thinking block (null for non-thinking models) |
final_answer |
Extracted final answer after thinking is removed |
finish_reason |
stop (completed) or length (truncated at max_tokens) |
prompt_tokens |
Number of tokens in the prompt |
completion_tokens |
Number of tokens generated |
temperature |
Sampling temperature used |
max_tokens |
Token generation limit |
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