messages listlengths 1 1 | ground_truth stringclasses 9 values | dataset stringclasses 1 value |
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[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is red. The 11-gon is then ro... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is uncolored, vertex 5 is blue, vertex 6 is uncolored, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is blue. Ho... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is uncolored, vertex 2 is blue, vertex 3 is red, vertex 4 is red, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is uncolored. How many valid coloring... | 0 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum number of red verti... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is red. What is the maximum number of red vert... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is uncolored, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid color... | 0 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is uncolored, vertex 7 is blue, vertex 8 is blue, vertex 9 is red. How many valid color... | 8 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is uncolored, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 10 is blue. How ... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is uncolored, vertex 5 is uncolored, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is red. How many valid coloring... | 0 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is red, vertex 9 is uncolored. How many valid colorin... | 1 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is uncolored, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is uncolored, vertex 10 is uncolored. How ... | 5 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is uncolored, vertex 3 is uncolored, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is uncolored. How... | 1 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is blue, vertex 9 is red, vertex 10 is uncolored. H... | 7 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 10 is red. Ho... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximum number of blue vert... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is blue, vertex 10 is red. How... | 1 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maxim... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colorin... | 3 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maximum ... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is red. What is the maximu... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. The 10-gon is then rotated clockwise ... | 2 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is blue. The 11-gon is then... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue ver... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is uncolored, vertex 5 is uncolored, vertex 6 is uncolored, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. How many valid color... | 0 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is uncolored, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is red. How many valid colori... | 3 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is red, vertex 10 is blue. How ... | 6 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue ver... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue ver... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is uncolored, vertex 9 is uncolored, vertex 10 is uncolored. Ho... | 0 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is uncolored. Ho... | 5 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is red, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is uncolored, vertex 9 is blue. How many valid colo... | 0 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is uncolored, vertex 10 is blue. How... | 2 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum number of blue vertic... | 2 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is red. What is the maximum number of red vert... | 5 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximu... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is uncolored, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is blue. How many valid colori... | 2 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 10 is uncolored. How ... | 0 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of red vert... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue v... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue. What is the maximum number of blue ve... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue, vertex 10 is red. What is the maximum... | 3 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximu... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is blue. How many valid colorin... | 3 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximu... | 3 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum number of blue vert... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maximu... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is red, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colori... | 1 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximum number of red vert... | 4 | MATH |
[
{
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is red. What is the maximum ... | 4 | MATH |
[
{
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is uncolored, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colorin... | 2 | MATH |
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