Datasets:
task_id stringlengths 26 34 | input stringlengths 189 1.32k | raw_output stringlengths 351 153k | thinking_content stringlengths 118 124k ⌀ | final_answer stringlengths 9 153k | finish_reason stringclasses 2
values | prompt_tokens int64 114 700 | completion_tokens int64 137 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... | analysisWe have system of equations with integers. Let's denote unknowns a,b,c positive integers with a≥b≥c.
Equations:
(1) a^2 - b^2 - c^2 + a b = 2011.
(2) a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc = -1997.
We need a.
Let's attempt to simplify. Let’s write in terms of differences maybe.
Let’s compute (2) maybe rewrit... | We have system of equations with integers. Let's denote unknowns a,b,c positive integers with a≥b≥c.
Equations:
(1) a^2 - b^2 - c^2 + a b = 2011.
(2) a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc = -1997.
We need a.
Let's attempt to simplify. Let’s write in terms of differences maybe.
Let’s compute (2) maybe rewrite as:
a... | First rewrite the two equations in a convenient form.
\[
\begin{cases}
a^2-b^2-c^2+ab=2011 \quad &(1)\\[2mm]
a^2+3b^2+3c^2-3ab-2ac-2bc=-1997 \quad &(2)
\end{cases}
\]
Subtract (1) from (2):
\[
4b^2+4c^2-4ab-2ac-2bc=-4008
\]
Divide by \(2\):
\[
2b^2+2c^2-2ab-ac-bc=-2004
\]
Let
\[
x=a-b\ge 0,\qquad y=a+b-2c\ge 0... | stop | 228 | 3,961 | 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... | analysisWe need to compute profit. She bakes 48 loaves. Cost per loaf 0.75. Total cost = 48 * 0.75 = 36. She sells half in morning at $2.50 each. Half of 48 = 24 loaves sold at 2.50 each. Revenue morning = 24 * 2.50 = 60.
Remaining after morning: 48 - 24 = 24 loaves.
Afternoon: sells two thirds of what she has left. ... | We need to compute profit. She bakes 48 loaves. Cost per loaf 0.75. Total cost = 48 * 0.75 = 36. She sells half in morning at $2.50 each. Half of 48 = 24 loaves sold at 2.50 each. Revenue morning = 24 * 2.50 = 60.
Remaining after morning: 48 - 24 = 24 loaves.
Afternoon: sells two thirds of what she has left. Two thir... | First compute the cost of making the bread.
\[
48\text{ loaves}\times \$0.75=\$36
\]
Now calculate the revenue from each sale.
**Morning:**
Half of 48 loaves are sold at \$2.50 each.
\[
\frac{48}{2}=24\text{ loaves}\quad\Rightarrow\quad 24\times \$2.50=\$60
\]
**Afternoon:**
Two thirds of the remaining 24 loav... | stop | 250 | 511 | 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... | analysisWe have set of six numbers: a1=m, a2=m+4, a3=m+10, a4=n+1, a5=n+2, a6=2n. They are not necessarily sorted. Condition: mean = n, median = n. Also m+10 < n+1 (strict). So m+10 < n+1 => m+9 < n. So n > m+9.
We need to find positive integers m,n satisfying these.
Mean: sum/6 = n => sum = 6n.
Compute sum: m + (m+... | We have set of six numbers: a1=m, a2=m+4, a3=m+10, a4=n+1, a5=n+2, a6=2n. They are not necessarily sorted. Condition: mean = n, median = n. Also m+10 < n+1 (strict). So m+10 < n+1 => m+9 < n. So n > m+9.
We need to find positive integers m,n satisfying these.
Mean: sum/6 = n => sum = 6n.
Compute sum: m + (m+4) + (m+... | The set is
\[
\{m,\;m+4,\;m+10,\;n+1,\;n+2,\;2n\}
\]
with \(m+10<n+1\).
---
### 1. Mean condition
\[
\frac{m+(m+4)+(m+10)+(n+1)+(n+2)+2n}{6}=n
\]
Sum the terms:
\[
m+(m+4)+(m+10)=3m+14,\qquad (n+1)+(n+2)+2n=4n+3
\]
Hence
\[
\frac{3m+14+4n+3}{6}=n\quad\Longrightarrow\quad 3m+4n+17=6n
\]
\[
3m+17=2n\quad... | stop | 204 | 2,895 | 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 $S_{i,j}\subseteq\{1,2,\ldots,2n\}$, for integers $i,j$ with $0\leq i,j\leq n$, such that:
$\bullet$ for all $0\leq i,j\leq n$, the set $S_{i,j}$ has $i+j$ elements; and
$\bullet$ $S_{i,j}\subseteq S_{k,l}$ whenever $0\leq... | analysisWe need to count number of ways to choose a family of sets S_{i,j} indexed by grid (i,j) with 0≤i,j≤n, total (n+1)^2 sets, each S_{i,j} subset of {1,...,2n}. Conditions: size |S_{i,j}| = i+j. And monotonicity: if i≤k and j≤l then S_{i,j} ⊆ S_{k,l}. So it's a lattice of sets with increasing sizes. Equivalent to ... | We need to count number of ways to choose a family of sets S_{i,j} indexed by grid (i,j) with 0≤i,j≤n, total (n+1)^2 sets, each S_{i,j} subset of {1,...,2n}. Conditions: size |S_{i,j}| = i+j. And monotonicity: if i≤k and j≤l then S_{i,j} ⊆ S_{k,l}. So it's a lattice of sets with increasing sizes. Equivalent to choose a... | Let
\[
S_{i,j}\subseteq\{1,2,\dots ,2n\}\qquad(0\le i,j\le n)
\]
satisfy
* \(|S_{i,j}|=i+j\) for all \(i,j\);
* \(S_{i,j}\subseteq S_{k,l}\) whenever \(i\le k,\;j\le l\).
--------------------------------------------------------------------
### 1. Birth cells
For an element \(x\in\{1,\dots ,2n\}\) let
\[
B(... | stop | 238 | 19,426 | 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 is closer to the center of the region than it is to the boundary of the region?
$\text{(A)}\frac{1}{4} \qquad \text{(B)}\frac{1}{3} \qquad \text{(C)}\frac{1}{2} \qquad \text{(D)}\frac{2}{3} \qquad \text{(E)}\frac{3}{4}$
... | analysisWe need probability that distance from center < distance to boundary. For a point at distance r from center, distance to boundary is R - r, where R is radius. Condition: r < R - r => 2r < R => r < R/2. So points within radius R/2. Probability = area of inner circle / area of whole circle = (π (R/2)^2) / (π R^2)... | We need probability that distance from center < distance to boundary. For a point at distance r from center, distance to boundary is R - r, where R is radius. Condition: r < R - r => 2r < R => r < R/2. So points within radius R/2. Probability = area of inner circle / area of whole circle = (π (R/2)^2) / (π R^2) = (R^2/... | Let the circle have radius \(R\).
For a point chosen at random, let its distance from the center be \(r\) (\(0\le r\le R\)).
The distance from the point to the boundary of the circle is the difference between the radius and the point’s distance from the center:
\[
\text{distance to boundary}=R-r.
\]
We want the pro... | stop | 200 | 387 | 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 the block is viewed so that three of its faces are visible, exactly $231$ of the 1-cm cubes cannot be seen. Find the smallest possible value of $N.$
Please reason step by step, and put your final answer within oxed{}. | analysisWe have a rectangular block made of N unit cubes. We view it such that three faces are visible. That means we look at the block from a corner, so we can see three mutually adjacent faces: front, top, right (for example). The cubes that cannot be seen are those that are not on any of these three faces. So they a... | We have a rectangular block made of N unit cubes. We view it such that three faces are visible. That means we look at the block from a corner, so we can see three mutually adjacent faces: front, top, right (for example). The cubes that cannot be seen are those that are not on any of these three faces. So they are inter... | Let the block have dimensions \(a\times b\times c\) (in unit‑cubes).
When we look at the block from a corner we can see the three faces that meet at that corner.
The cubes that are **not** on any of these three faces are the ones that cannot be seen.
---
### 1. Counting the invisible cubes
The number of cubes o... | stop | 147 | 6,760 | 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) | "analysisWe need area of smallest region bounded by y=|x| and circle x^2 + y^2 = 4. The circle radiu(...TRUNCATED) | "We need area of smallest region bounded by y=|x| and circle x^2 + y^2 = 4. The circle radius 2 cent(...TRUNCATED) | "The circle \\(x^{2}+y^{2}=4\\) intersects the V‑shaped graph \\(y=|x|\\) at \n\\[\nx=\\pm\\sqrt{(...TRUNCATED) | stop | 191 | 2,549 | 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) | "analysisWe need compute (2,12,9) = 2/12 + 12/9 + 9/2. Compute: 2/12 = 1/6 ≈ 0.1666667. 12/9 = 4/3(...TRUNCATED) | "We need compute (2,12,9) = 2/12 + 12/9 + 9/2. Compute: 2/12 = 1/6 ≈ 0.1666667. 12/9 = 4/3 ≈ 1.3(...TRUNCATED) | "To evaluate \\((2,12,9)\\) we use the definition \n\n\\[\n(a,b,c)=\\frac{a}{b}+\\frac{b}{c}+\\frac(...TRUNCATED) | stop | 205 | 353 | 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) | "analysisWe have a cube of side n units, painted on all six faces, then cut into n^3 unit cubes. We (...TRUNCATED) | "We have a cube of side n units, painted on all six faces, then cut into n^3 unit cubes. We need to (...TRUNCATED) | "The big cube has side length \\(n\\). \nAfter painting and cutting, we have \\(n^3\\) unit cubes, (...TRUNCATED) | stop | 199 | 1,159 | 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) | "analysisWe need to analyze relationships between side, perimeter, area, circumradius for equilatera(...TRUNCATED) | "We need to analyze relationships between side, perimeter, area, circumradius for equilateral triang(...TRUNCATED) | "For an equilateral triangle with side \\(s\\):\n\n\\[\n\\begin{aligned}\n\\text{Perimeter }&=3s,\\\(...TRUNCATED) | stop | 287 | 1,089 | 0 | 32,768 |
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openai/gpt-oss-20b — creativemath-with-answers
Model outputs from the micro-creativity inference suite.
- Model:
openai/gpt-oss-20b - 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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