messages listlengths 1 1 | ground_truth stringclasses 10
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{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 1, from vertex 5 to vertex 3, from vertex 6 to vertex 4, from vertex 8 to vertex 6, from vertex 8 to vertex 4, from vertex 3 to vertex 7, from vertex 5 to vertex 2, and... | 6 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 11, from vertex 2 to vertex 8, from vertex 3 to vertex 7, from vertex 3 to vertex 1, from vertex 8 to vertex 1, and from vertex 3 to vertex 9. How many distinct pairs... | 3 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 1, from vertex 1 to vertex 4, from vertex 5 to vertex 3, from vertex 1 to vertex 3, from vertex 2 to vertex 6, from vertex 6 to vertex 3, from vertex 5 to vertex 2, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 2, from vertex 4 to vertex 6, from vertex 2 to vertex 6, from vertex 6 to vertex 10, from vertex 1 to vertex 7, from vertex 1 to vertex 3, and from vertex 3 to vertex... | 4 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 1, from vertex 7 to vertex 3, from vertex 6 to vertex 2, from vertex 4 to vertex 11, from vertex 8 to vertex 10, from vertex 7 to vertex 5, from vertex 3 to vertex 8,... | 3 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 3, from vertex 13 to vertex 2, from vertex 7 to vertex 13, from vertex 9 to vertex 5, from vertex 8 to vertex 1, from vertex 11 to vertex 2, and from vertex 10 to ver... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 9, from vertex 13 to vertex 3, from vertex 6 to vertex 11, from vertex 9 to vertex 6, from vertex 12 to vertex 1, from vertex 3 to vertex 10, and from vertex 1 to ver... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 10, from vertex 2 to vertex 9, from vertex 7 to vertex 3, from vertex 5 to vertex 1, from vertex 10 to vertex 5, from vertex 7 to vertex 1, and from vertex 2 to verte... | 2 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 8, from vertex 3 to vertex 5, from vertex 2 to vertex 4, from vertex 5 to vertex 2, from vertex 8 to vertex 6, and from vertex 4 to vertex 8. How many distinct pairs of... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 11, from vertex 2 to vertex 11, from vertex 3 to vertex 9, from vertex 10 to vertex 7, from vertex 4 to vertex 9, from vertex 1 to vertex 4, from vertex 9 to vertex 1... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 1, from vertex 5 to vertex 1, from vertex 5 to vertex 7, from vertex 4 to vertex 6, from vertex 3 to vertex 1, from vertex 8 to vertex 4, from vertex 2 to vertex 6, fro... | 10 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 5, from vertex 7 to vertex 3, from vertex 8 to vertex 2, from vertex 8 to vertex 5, from vertex 5 to vertex 7, from vertex 4 to vertex 6, from vertex 4 to vertex 8, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 6, from vertex 7 to vertex 2, from vertex 9 to vertex 5, from vertex 6 to vertex 10, from vertex 8 to vertex 1, from vertex 6 to vertex 1, from vertex 3 to vertex 10,... | 4 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 4, from vertex 10 to vertex 4, from vertex 4 to vertex 9, from vertex 5 to vertex 1, from vertex 7 to vertex 9, and from vertex 7 to vertex 4. How many distinct pairs... | 3 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 11 to vertex 4, from vertex 13 to vertex 7, from vertex 13 to vertex 9, from vertex 5 to vertex 2, from vertex 2 to vertex 6, from vertex 12 to vertex 6, and from vertex 10 to ve... | 2 | MATH |
[
{
"content": "Suppose you have a 13-gon, with vertices numbered 1 through 13 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 13, from vertex 4 to vertex 2, from vertex 13 to vertex 5, from vertex 12 to vertex 7, from vertex 7 to vertex 2, from vertex 8 to vertex 5, from vertex 7 to vertex 1... | 0 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 2, from vertex 2 to vertex 4, from vertex 1 to vertex 5, from vertex 5 to vertex 3, from vertex 3 to vertex 1, from vertex 4 to vertex 6, from vertex 5 to vertex 2, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 10 to vertex 14, from vertex 10 to vertex 2, from vertex 4 to vertex 9, from vertex 14 to vertex 4, from vertex 7 to vertex 3, from vertex 4 to vertex 12, from vertex 11 to verte... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 13 to vertex 5, from vertex 5 to vertex 7, from vertex 4 to vertex 7, from vertex 2 to vertex 14, from vertex 3 to vertex 6, from vertex 1 to vertex 3, and from vertex 8 to verte... | 3 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 6, from vertex 11 to vertex 3, from vertex 9 to vertex 12, from vertex 3 to vertex 6, from vertex 9 to vertex 3, from vertex 10 to vertex 8, from vertex 6 to vertex 1... | 4 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 1, from vertex 10 to vertex 5, from vertex 1 to vertex 10, from vertex 5 to vertex 12, from vertex 14 to vertex 7, from vertex 3 to vertex 14, from vertex 13 to verte... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 7 to vertex 5, from vertex 4 to vertex 2, from vertex 1 to vertex 4, from vertex 8 to vertex 4, from vertex 1 to vertex 3, from vertex 1 to vertex 6, and from vertex 3 to vertex 5.... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 7, from vertex 2 to vertex 7, from vertex 4 to vertex 8, from vertex 5 to vertex 7, from vertex 5 to vertex 2, from vertex 6 to vertex 8, and from vertex 1 to vertex 3.... | 1 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 9, from vertex 1 to vertex 10, from vertex 4 to vertex 2, from vertex 6 to vertex 14, from vertex 10 to vertex 7, from vertex 1 to vertex 13, from vertex 10 to vertex... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 5, from vertex 4 to vertex 1, from vertex 6 to vertex 8, from vertex 1 to vertex 6, from vertex 6 to vertex 2, from vertex 4 to vertex 6, and from vertex 7 to vertex 4.... | 2 | MATH |
[
{
"content": "Suppose you have a 13-gon, with vertices numbered 1 through 13 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 6, from vertex 11 to vertex 2, from vertex 6 to vertex 2, from vertex 11 to vertex 3, from vertex 5 to vertex 3, and from vertex 8 to vertex 11. How many distinct pai... | 0 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 3, from vertex 12 to vertex 9, from vertex 6 to vertex 12, from vertex 4 to vertex 8, from vertex 3 to vertex 9, and from vertex 12 to vertex 4. How many distinct pai... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 5, from vertex 11 to vertex 13, from vertex 9 to vertex 3, from vertex 1 to vertex 10, from vertex 13 to vertex 6, from vertex 2 to vertex 12, and from vertex 2 to ve... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 10, from vertex 2 to vertex 5, from vertex 4 to vertex 9, from vertex 8 to vertex 2, from vertex 2 to vertex 6, from vertex 5 to vertex 10, from vertex 3 to vertex 5,... | 6 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 2, from vertex 6 to vertex 3, from vertex 2 to vertex 5, from vertex 2 to vertex 4, from vertex 5 to vertex 3, and from vertex 1 to vertex 5. How many distinct pairs of... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 11 to vertex 5, from vertex 4 to vertex 12, from vertex 4 to vertex 2, from vertex 10 to vertex 7, from vertex 3 to vertex 13, from vertex 5 to vertex 7, from vertex 10 to vertex... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 11, from vertex 2 to vertex 4, from vertex 9 to vertex 12, from vertex 11 to vertex 2, from vertex 6 to vertex 9, from vertex 1 to vertex 4, from vertex 8 to vertex 2... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 4, from vertex 12 to vertex 9, from vertex 9 to vertex 1, from vertex 12 to vertex 4, from vertex 5 to vertex 9, from vertex 6 to vertex 11, from vertex 4 to vertex 7... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 10 to vertex 13, from vertex 9 to vertex 4, from vertex 12 to vertex 1, from vertex 7 to vertex 13, from vertex 4 to vertex 7, from vertex 8 to vertex 11, and from vertex 13 to v... | 3 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 3, from vertex 4 to vertex 1, from vertex 5 to vertex 1, from vertex 5 to vertex 2, from vertex 5 to vertex 3, from vertex 6 to vertex 3, from vertex 6 to vertex 4, and... | 5 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 7, from vertex 7 to vertex 1, from vertex 1 to vertex 6, from vertex 1 to vertex 8, from vertex 5 to vertex 3, from vertex 5 to vertex 9, from vertex 9 to vertex 3, a... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 6, from vertex 4 to vertex 2, from vertex 11 to vertex 8, from vertex 4 to vertex 6, from vertex 8 to vertex 1, from vertex 9 to vertex 12, from vertex 1 to vertex 11... | 1 | MATH |
[
{
"content": "Suppose you have a 7-gon, with vertices numbered 1 through 7 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 4, from vertex 7 to vertex 4, from vertex 1 to vertex 5, from vertex 3 to vertex 6, from vertex 7 to vertex 3, and from vertex 1 to vertex 3. How many distinct pairs of... | 0 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 2, from vertex 8 to vertex 13, from vertex 7 to vertex 2, from vertex 9 to vertex 11, from vertex 3 to vertex 12, from vertex 11 to vertex 5, and from vertex 5 to ver... | 3 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 3, from vertex 10 to vertex 7, from vertex 7 to vertex 9, from vertex 8 to vertex 11, from vertex 5 to vertex 2, from vertex 4 to vertex 6, from vertex 11 to vertex 1... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 9, from vertex 3 to vertex 12, from vertex 4 to vertex 10, from vertex 8 to vertex 6, from vertex 6 to vertex 4, from vertex 4 to vertex 8, and from vertex 10 to vert... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 1, from vertex 4 to vertex 9, from vertex 4 to vertex 1, from vertex 10 to vertex 2, from vertex 8 to vertex 4, from vertex 4 to vertex 6, from vertex 10 to vertex 5,... | 4 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 2, from vertex 7 to vertex 3, from vertex 1 to vertex 6, from vertex 1 to vertex 7, from vertex 1 to vertex 9, from vertex 7 to vertex 5, from vertex 10 to vertex 8, ... | 2 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 1, from vertex 10 to vertex 5, from vertex 4 to vertex 1, from vertex 3 to vertex 6, from vertex 10 to vertex 4, from vertex 8 to vertex 5, from vertex 7 to vertex 1,... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 1, from vertex 5 to vertex 2, from vertex 6 to vertex 1, from vertex 2 to vertex 7, from vertex 4 to vertex 6, from vertex 3 to vertex 5, and from vertex 2 to vertex 4.... | 2 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 4, from vertex 3 to vertex 1, from vertex 6 to vertex 2, from vertex 2 to vertex 5, from vertex 6 to vertex 3, from vertex 4 to vertex 1, and from vertex 5 to vertex 3.... | 4 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 9, from vertex 4 to vertex 7, from vertex 12 to vertex 8, from vertex 1 to vertex 4, from vertex 11 to vertex 1, from vertex 2 to vertex 13, and from vertex 12 to ver... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 1, from vertex 14 to vertex 6, from vertex 7 to vertex 9, from vertex 4 to vertex 1, from vertex 3 to vertex 14, from vertex 6 to vertex 2, and from vertex 10 to vert... | 1 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 7, from vertex 7 to vertex 5, from vertex 3 to vertex 8, from vertex 4 to vertex 6, from vertex 2 to vertex 6, from vertex 5 to vertex 1, from vertex 4 to vertex 1, and... | 4 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 12, from vertex 11 to vertex 8, from vertex 1 to vertex 11, from vertex 9 to vertex 14, from vertex 8 to vertex 3, from vertex 5 to vertex 2, and from vertex 4 to ver... | 2 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 14 to vertex 3, from vertex 10 to vertex 12, from vertex 2 to vertex 6, from vertex 7 to vertex 1, from vertex 9 to vertex 3, and from vertex 13 to vertex 6. How many distinct pa... | 1 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 8, from vertex 5 to vertex 8, from vertex 1 to vertex 7, from vertex 6 to vertex 2, from vertex 7 to vertex 2, from vertex 3 to vertex 7, from vertex 4 to vertex 8, fro... | 4 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 12, from vertex 5 to vertex 3, from vertex 9 to vertex 5, from vertex 4 to vertex 6, from vertex 2 to vertex 7, from vertex 6 to vertex 12, and from vertex 3 to verte... | 2 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 4, from vertex 2 to vertex 5, from vertex 4 to vertex 1, from vertex 5 to vertex 1, from vertex 3 to vertex 5, from vertex 4 to vertex 6, from vertex 1 to vertex 3, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 14, from vertex 1 to vertex 8, from vertex 10 to vertex 8, from vertex 5 to vertex 12, from vertex 10 to vertex 13, from vertex 11 to vertex 7, and from vertex 12 to ... | 0 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 11 to vertex 6, from vertex 10 to vertex 7, from vertex 6 to vertex 12, from vertex 6 to vertex 13, from vertex 3 to vertex 11, from vertex 3 to vertex 10, and from vertex 4 to v... | 0 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 2, from vertex 1 to vertex 4, from vertex 2 to vertex 4, from vertex 6 to vertex 4, from vertex 1 to vertex 5, and from vertex 5 to vertex 3. How many distinct pairs of... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 12 to vertex 3, from vertex 9 to vertex 3, from vertex 10 to vertex 1, from vertex 5 to vertex 7, from vertex 3 to vertex 10, from vertex 7 to vertex 12, and from vertex 5 to ver... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 7, from vertex 10 to vertex 5, from vertex 2 to vertex 5, from vertex 6 to vertex 3, from vertex 1 to vertex 7, from vertex 7 to vertex 3, and from vertex 2 to vertex... | 2 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 10 to vertex 6, from vertex 11 to vertex 5, from vertex 4 to vertex 8, from vertex 3 to vertex 12, from vertex 7 to vertex 9, from vertex 9 to vertex 4, and from vertex 12 to ver... | 0 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 7, from vertex 4 to vertex 1, from vertex 7 to vertex 5, from vertex 5 to vertex 1, from vertex 4 to vertex 6, from vertex 5 to vertex 3, from vertex 6 to vertex 3, and... | 6 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 8, from vertex 5 to vertex 1, from vertex 1 to vertex 4, from vertex 8 to vertex 6, from vertex 9 to vertex 4, and from vertex 6 to vertex 4. How many distinct pairs ... | 1 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 6, from vertex 1 to vertex 4, from vertex 3 to vertex 6, from vertex 5 to vertex 3, from vertex 2 to vertex 6, and from vertex 2 to vertex 5. How many distinct pairs of... | 3 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 6, from vertex 10 to vertex 2, from vertex 5 to vertex 9, from vertex 8 to vertex 5, from vertex 8 to vertex 6, and from vertex 7 to vertex 1. How many distinct pairs... | 3 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 9, from vertex 5 to vertex 2, from vertex 5 to vertex 1, from vertex 8 to vertex 12, from vertex 2 to vertex 4, from vertex 8 to vertex 1, from vertex 12 to vertex 3,... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 8, from vertex 2 to vertex 5, from vertex 4 to vertex 7, from vertex 5 to vertex 8, from vertex 6 to vertex 1, from vertex 4 to vertex 8, from vertex 4 to vertex 6, fro... | 5 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 6, from vertex 5 to vertex 1, from vertex 8 to vertex 4, from vertex 5 to vertex 2, from vertex 1 to vertex 6, from vertex 3 to vertex 1, from vertex 8 to vertex 2, and... | 5 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 5, from vertex 5 to vertex 2, from vertex 5 to vertex 3, from vertex 2 to vertex 4, from vertex 4 to vertex 1, from vertex 6 to vertex 3, and from vertex 2 to vertex 6.... | 4 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 4, from vertex 3 to vertex 5, from vertex 5 to vertex 2, from vertex 4 to vertex 1, from vertex 2 to vertex 4, and from vertex 6 to vertex 3. How many distinct pairs of... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 3, from vertex 2 to vertex 7, from vertex 3 to vertex 5, from vertex 5 to vertex 1, from vertex 7 to vertex 5, from vertex 4 to vertex 7, from vertex 8 to vertex 6, and... | 3 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 6, from vertex 2 to vertex 6, from vertex 3 to vertex 6, from vertex 5 to vertex 1, from vertex 5 to vertex 3, from vertex 4 to vertex 1, from vertex 1 to vertex 3, and... | 4 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 6, from vertex 2 to vertex 8, from vertex 3 to vertex 7, from vertex 8 to vertex 4, from vertex 4 to vertex 7, from vertex 2 to vertex 4, from vertex 1 to vertex 7, and... | 4 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 7, from vertex 1 to vertex 9, from vertex 1 to vertex 3, from vertex 10 to vertex 4, from vertex 8 to vertex 4, from vertex 1 to vertex 5, from vertex 4 to vertex 9, ... | 3 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 11, from vertex 2 to vertex 7, from vertex 4 to vertex 1, from vertex 11 to vertex 4, from vertex 14 to vertex 9, from vertex 8 to vertex 12, and from vertex 11 to ve... | 2 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 6, from vertex 10 to vertex 3, from vertex 10 to vertex 6, from vertex 8 to vertex 6, from vertex 2 to vertex 6, from vertex 2 to vertex 5, and from vertex 1 to verte... | 1 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 13, from vertex 6 to vertex 1, from vertex 10 to vertex 7, from vertex 2 to vertex 6, from vertex 10 to vertex 3, and from vertex 10 to vertex 12. How many distinct p... | 0 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 4, from vertex 3 to vertex 8, from vertex 5 to vertex 3, from vertex 3 to vertex 6, from vertex 6 to vertex 4, and from vertex 1 to vertex 7. How many distinct pairs of... | 1 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 9 to vertex 1, from vertex 8 to vertex 14, from vertex 6 to vertex 2, from vertex 10 to vertex 8, from vertex 1 to vertex 11, from vertex 10 to vertex 14, from vertex 5 to vertex... | 0 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 12 to vertex 9, from vertex 11 to vertex 6, from vertex 8 to vertex 10, from vertex 4 to vertex 6, from vertex 11 to vertex 2, from vertex 5 to vertex 10, from vertex 5 to vertex... | 3 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 7, from vertex 4 to vertex 11, from vertex 4 to vertex 10, from vertex 7 to vertex 12, from vertex 2 to vertex 11, from vertex 5 to vertex 2, from vertex 10 to vertex... | 3 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 5, from vertex 4 to vertex 6, from vertex 4 to vertex 2, from vertex 5 to vertex 1, from vertex 5 to vertex 3, and from vertex 3 to vertex 1. How many distinct pairs of... | 2 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 6, from vertex 5 to vertex 2, from vertex 2 to vertex 6, from vertex 4 to vertex 2, from vertex 6 to vertex 3, from vertex 5 to vertex 3, from vertex 3 to vertex 1, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 3, from vertex 12 to vertex 9, from vertex 6 to vertex 12, from vertex 4 to vertex 8, from vertex 3 to vertex 9, and from vertex 12 to vertex 4. How many distinct pai... | 2 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 6, from vertex 1 to vertex 4, from vertex 6 to vertex 4, from vertex 2 to vertex 4, from vertex 6 to vertex 3, from vertex 2 to vertex 5, and from vertex 5 to vertex 1.... | 4 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 8, from vertex 8 to vertex 3, from vertex 7 to vertex 3, from vertex 7 to vertex 1, from vertex 1 to vertex 3, and from vertex 4 to vertex 7. How many distinct pairs of... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 5, from vertex 4 to vertex 10, from vertex 7 to vertex 4, from vertex 7 to vertex 10, from vertex 10 to vertex 6, from vertex 2 to vertex 7, from vertex 10 to vertex ... | 4 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 9, from vertex 6 to vertex 9, from vertex 8 to vertex 11, from vertex 1 to vertex 11, from vertex 1 to vertex 3, and from vertex 8 to vertex 3. How many distinct pair... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 5, from vertex 6 to vertex 10, from vertex 2 to vertex 4, from vertex 9 to vertex 3, from vertex 8 to vertex 5, from vertex 10 to vertex 5, and from vertex 2 to verte... | 1 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 7, from vertex 8 to vertex 6, from vertex 3 to vertex 1, from vertex 1 to vertex 7, from vertex 4 to vertex 8, from vertex 2 to vertex 4, from vertex 6 to vertex 3, and... | 4 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 7, from vertex 8 to vertex 3, from vertex 12 to vertex 4, from vertex 2 to vertex 10, from vertex 6 to vertex 10, and from vertex 10 to vertex 3. How many distinct pa... | 0 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 5, from vertex 2 to vertex 6, from vertex 4 to vertex 2, from vertex 2 to vertex 8, from vertex 8 to vertex 5, from vertex 2 to vertex 7, and from vertex 3 to vertex 6.... | 3 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 3, from vertex 6 to vertex 8, from vertex 7 to vertex 4, from vertex 7 to vertex 3, from vertex 8 to vertex 3, from vertex 9 to vertex 7, from vertex 5 to vertex 10, ... | 3 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 13 to vertex 9, from vertex 4 to vertex 2, from vertex 11 to vertex 13, from vertex 1 to vertex 4, from vertex 5 to vertex 12, and from vertex 11 to vertex 4. How many distinct p... | 2 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 6, from vertex 2 to vertex 6, from vertex 2 to vertex 4, from vertex 1 to vertex 3, from vertex 5 to vertex 2, from vertex 1 to vertex 4, from vertex 1 to vertex 5, fro... | 6 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 13, from vertex 10 to vertex 14, from vertex 6 to vertex 8, from vertex 14 to vertex 6, from vertex 12 to vertex 3, from vertex 7 to vertex 12, from vertex 2 to verte... | 1 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 1, from vertex 10 to vertex 3, from vertex 7 to vertex 9, from vertex 10 to vertex 2, from vertex 8 to vertex 1, from vertex 9 to vertex 2, and from vertex 2 to verte... | 3 | MATH |
[
{
"content": "Suppose you have a 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 11, from vertex 8 to vertex 1, from vertex 2 to vertex 10, from vertex 2 to vertex 8, from vertex 8 to vertex 6, from vertex 8 to vertex 10, from vertex 3 to vertex 8... | 3 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 5, from vertex 7 to vertex 2, from vertex 8 to vertex 5, from vertex 7 to vertex 3, from vertex 5 to vertex 3, from vertex 1 to vertex 4, from vertex 1 to vertex 6, fro... | 4 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 5, from vertex 2 to vertex 6, from vertex 4 to vertex 2, from vertex 2 to vertex 8, from vertex 8 to vertex 5, from vertex 2 to vertex 7, and from vertex 3 to vertex 6.... | 3 | MATH |
[
{
"content": "Suppose you have a 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 1 to vertex 5, from vertex 5 to vertex 2, from vertex 5 to vertex 3, from vertex 2 to vertex 4, from vertex 4 to vertex 1, from vertex 6 to vertex 3, from vertex 2 to vertex 6, fro... | 6 | MATH |
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