messages listlengths 1 1 | ground_truth stringclasses 7
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{
"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 2 to vertex 4, from vertex 4 to vertex 1, from vertex 4 to vertex 6, from vertex 6 to vertex 2, from vertex 3 to vertex 5, and from vertex 3 to vertex 1.... | 2 | 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 2 to vertex 5, from vertex 3 to vertex 6, from vertex 4 to vertex 2, from vertex 5 to vertex 3, from vertex 6 to vertex 4, and from vertex 6 to vertex 2.... | 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 3, from vertex 4 to vertex 8, from vertex 8 to vertex 6, from vertex 2 to vertex 5, from vertex 7 to vertex 5, from vertex 5 to vertex 3, and from vertex 4 to vertex 6.... | 4 | 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 3, from vertex 3 to vertex 7, from vertex 2 to vertex 6, from vertex 8 to vertex 4, from vertex 7 to vertex 2, and from vertex 6 to vertex 4. 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 10 to vertex 2, from vertex 10 to vertex 13, from vertex 5 to vertex 7, from vertex 14 to vertex 10, from vertex 11 to vertex 9, from vertex 11 to vertex 1, and from vertex 1 to ... | 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 1, from vertex 7 to vertex 5, from vertex 11 to vertex 5, from vertex 5 to vertex 8, from vertex 12 to vertex 5, and from vertex 8 to vertex 1. How many distinct pair... | 1 | 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 3, from vertex 7 to vertex 10, from vertex 14 to vertex 6, from vertex 7 to vertex 11, from vertex 6 to vertex 4, from vertex 12 to vertex 14, and from vertex 4 to ve... | 1 | 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 2, from vertex 1 to vertex 3, from vertex 2 to vertex 4, from vertex 2 to vertex 6, from vertex 4 to vertex 6, from vertex 5 to vertex 3, and from vertex 4 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 6 to vertex 2, from vertex 3 to vertex 5, from vertex 8 to vertex 3, from vertex 5 to vertex 1, from vertex 2 to vertex 7, and from vertex 1 to vertex 6. 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 7, from vertex 1 to vertex 13, from vertex 1 to vertex 3, from vertex 4 to vertex 13, from vertex 12 to vertex 10, from vertex 2 to vertex 13, and from vertex 13 to v... | 2 | 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 7 to vertex 5, from vertex 3 to vertex 10, from vertex 3 to vertex 8, from vertex 4 to vertex 10, from vertex 5 to vertex 3, and from vertex 2 to vert... | 3 | 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 4 to vertex 6, from vertex 4 to vertex 2, from vertex 2 to vertex 6, from vertex 1 to vertex 4, and from vertex 5 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 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 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 1 to vertex 8, from vertex 12 to vertex 7, from vertex 12 to vertex 5, from vertex 10 to vertex 3, from vertex 4 to vertex 11, and from vertex 11 to vertex 8. How many distinct p... | 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 3, from vertex 12 to vertex 10, from vertex 12 to vertex 9, from vertex 11 to vertex 1, from vertex 12 to vertex 4, and from vertex 1 to vertex 6. How many distinct p... | 0 | 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 3, from vertex 10 to vertex 6, from vertex 2 to vertex 8, from vertex 6 to vertex 1, from vertex 3 to vertex 1, from vertex 9 to vertex 7, and from vertex 6 to vertex... | 1 | 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 10, from vertex 11 to vertex 8, from vertex 3 to vertex 11, from vertex 7 to vertex 1, from vertex 6 to vertex 14, and from vertex 7 to vertex 14. How many distinct ... | 1 | 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 4, from vertex 11 to vertex 5, from vertex 2 to vertex 9, from vertex 3 to vertex 9, from vertex 8 to vertex 13, and from vertex 10 to vertex 4. How many distinct pai... | 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 8, from vertex 12 to vertex 9, from vertex 11 to vertex 1, from vertex 3 to vertex 11, from vertex 11 to vertex 4, from vertex 8 to vertex 4, and from vertex 2 to ver... | 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 4, from vertex 7 to vertex 3, from vertex 7 to vertex 4, from vertex 5 to vertex 7, from vertex 4 to vertex 8, from vertex 4 to vertex 6, and from vertex 5 to vertex 1.... | 4 | 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 4 to vertex 6, from vertex 3 to vertex 1, from vertex 2 to vertex 4, from vertex 3 to vertex 5, and from vertex 6 to vertex 3. 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 2, from vertex 3 to vertex 5, from vertex 4 to vertex 6, from vertex 5 to vertex 2, from vertex 1 to vertex 3, from vertex 6 to vertex 2, and from vertex 6 to vertex 3.... | 3 | 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 14, from vertex 12 to vertex 10, from vertex 6 to vertex 2, from vertex 14 to vertex 9, from vertex 11 to vertex 13, from vertex 2 to vertex 10, and from vertex 10 to... | 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 4, from vertex 11 to vertex 2, from vertex 11 to vertex 1, from vertex 5 to vertex 7, from vertex 9 to vertex 3, and from vertex 2 to vertex 7. How many distinct pai... | 0 | MATH |
[
{
"content": "Suppose you have a 10-gon, with vertices numbered 1 through 10 in counterclockwise order. Draw the diagonal from vertex 10 to vertex 4, from vertex 7 to vertex 1, from vertex 3 to vertex 1, from vertex 2 to vertex 5, from vertex 1 to vertex 4, and from vertex 5 to vertex 7. How many distinct pairs... | 1 | MATH |
[
{
"content": "Suppose you have a 9-gon, with vertices numbered 1 through 9 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 5, from vertex 6 to vertex 9, from vertex 4 to vertex 7, from vertex 6 to vertex 4, from vertex 4 to vertex 8, from vertex 1 to vertex 8, and from vertex 5 to vertex 1.... | 0 | 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 4, from vertex 3 to vertex 1, from vertex 8 to vertex 1, from vertex 8 to vertex 3, from vertex 7 to vertex 1, from vertex 9 to vertex 4, and from vertex 11 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 7 to vertex 5, from vertex 11 to vertex 3, from vertex 1 to vertex 10, from vertex 12 to vertex 2, from vertex 11 to vertex 6, and from vertex 10 to vertex 6. How many distinct p... | 1 | 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 10, from vertex 7 to vertex 2, from vertex 2 to vertex 4, from vertex 1 to vertex 4, from vertex 14 to vertex 12, and from vertex 2 to vertex 5. How many distinct pa... | 1 | 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 5, from vertex 10 to vertex 4, from vertex 8 to vertex 1, from vertex 1 to vertex 9, from vertex 4 to vertex 7, and from vertex 6 to vertex 8. How many distinct pairs... | 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 4, from vertex 7 to vertex 1, from vertex 8 to vertex 4, from vertex 6 to vertex 4, from vertex 6 to vertex 2, and from vertex 4 to vertex 7. 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 4 to vertex 6, from vertex 3 to vertex 6, from vertex 5 to vertex 8, from vertex 7 to vertex 4, from vertex 3 to vertex 8, from vertex 7 to vertex 1, and from vertex 1 to vertex 5.... | 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 10, from vertex 8 to vertex 5, from vertex 8 to vertex 2, from vertex 4 to vertex 14, from vertex 14 to vertex 6, from vertex 6 to vertex 9, and from vertex 8 to ver... | 1 | 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 12, from vertex 4 to vertex 10, from vertex 2 to vertex 12, from vertex 7 to vertex 10, from vertex 4 to vertex 8, and from vertex 8 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 7 to vertex 1, from vertex 4 to vertex 8, from vertex 2 to vertex 8, from vertex 8 to vertex 6, from vertex 7 to vertex 4, and from vertex 4 to vertex 6.... | 3 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 12 to vertex 10, from vertex 12 to vertex 4, from vertex 4 to vertex 7, from vertex 5 to vertex 14, from vertex 3 to vertex 6, from vertex 13 to vertex 2, and from vertex 9 to ve... | 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 1, from vertex 7 to vertex 4, from vertex 2 to vertex 12, from vertex 4 to vertex 8, from vertex 12 to vertex 7, from vertex 8 to vertex 10, and from vertex 7 to ver... | 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 6, from vertex 7 to vertex 4, from vertex 8 to vertex 3, from vertex 12 to vertex 8, from vertex 9 to vertex 3, from vertex 4 to vertex 2, and from vertex 9 to vertex... | 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 1, from vertex 2 to vertex 5, from vertex 6 to vertex 4, from vertex 4 to vertex 2, from vertex 3 to vertex 5, and from vertex 5 to vertex 1. 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 1 to vertex 5, from vertex 11 to vertex 8, from vertex 3 to vertex 8, from vertex 9 to vertex 11, from vertex 9 to vertex 1, from vertex 5 to vertex 8, and from vertex 7 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 5 to vertex 1, from vertex 3 to vertex 9, from vertex 7 to vertex 5, from vertex 5 to vertex 10, from vertex 9 to vertex 5, and from vertex 6 to vertex 4. How many distinct pairs... | 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 10, from vertex 6 to vertex 3, from vertex 2 to vertex 5, from vertex 9 to vertex 3, from vertex 10 to vertex 5, and from vertex 10 to vertex 7. How many distinct pai... | 2 | MATH |
[
{
"content": "Suppose you have a 8-gon, with vertices numbered 1 through 8 in counterclockwise order. Draw the diagonal from vertex 5 to vertex 7, from vertex 3 to vertex 1, from vertex 8 to vertex 4, from vertex 1 to vertex 7, from vertex 2 to vertex 7, from vertex 6 to vertex 3, and from vertex 7 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 4 to vertex 1, from vertex 5 to vertex 8, from vertex 3 to vertex 6, from vertex 4 to vertex 8, from vertex 4 to vertex 7, from vertex 3 to vertex 7, and from vertex 1 to vertex 7.... | 3 | 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 6 to vertex 9, from vertex 8 to vertex 5, from vertex 2 to vertex 5, from vertex 10 to vertex 5, from vertex 4 to vertex 1, and from vertex 3 to vertex... | 0 | 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 12-gon, with vertices numbered 1 through 12 in counterclockwise order. Draw the diagonal from vertex 2 to vertex 9, from vertex 11 to vertex 8, from vertex 10 to vertex 2, from vertex 10 to vertex 8, from vertex 10 to vertex 4, and from vertex 6 to vertex 2. How many distinct pa... | 2 | 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 2, from vertex 1 to vertex 5, from vertex 3 to vertex 1, from vertex 6 to vertex 3, from vertex 5 to vertex 3, from vertex 2 to vertex 6, and from vertex 4 to vertex 6.... | 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 2, from vertex 7 to vertex 2, from vertex 6 to vertex 4, from vertex 6 to vertex 3, from vertex 5 to vertex 8, and from vertex 7 to vertex 4. How many distinct pairs of... | 2 | 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 6, from vertex 4 to vertex 8, from vertex 6 to vertex 4, from vertex 1 to vertex 6, from vertex 3 to vertex 8, from vertex 1 to vertex 3, and from vertex 5 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 14 to vertex 9, from vertex 13 to vertex 4, from vertex 7 to vertex 5, from vertex 1 to vertex 12, from vertex 9 to vertex 7, and from vertex 4 to vertex 12. How many distinct pa... | 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 4 to vertex 1, from vertex 2 to vertex 5, from vertex 1 to vertex 3, from vertex 5 to vertex 1, from vertex 6 to vertex 2, and from vertex 6 to vertex 3.... | 4 | 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 4, from vertex 6 to vertex 3, from vertex 3 to vertex 1, from vertex 4 to vertex 2, from vertex 3 to vertex 5, from vertex 5 to vertex 2, and from vertex 1 to vertex 5.... | 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 6, from vertex 2 to vertex 11, from vertex 13 to vertex 3, from vertex 12 to vertex 2, from vertex 5 to vertex 8, and from vertex 5 to vertex 11. How many distinct pa... | 0 | 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 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 3, from vertex 2 to vertex 4, from vertex 1 to vertex 5, from vertex 4 to vertex 6, from vertex 4 to vertex 1, from vertex 1 to vertex 3, and from vertex 6 to vertex 2.... | 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 8, from vertex 7 to vertex 10, from vertex 9 to vertex 6, from vertex 10 to vertex 5, from vertex 7 to vertex 1, and from vertex 12 to vertex 10. How many distinct pa... | 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 8, from vertex 2 to vertex 10, from vertex 7 to vertex 5, from vertex 7 to vertex 9, from vertex 7 to vertex 10, from vertex 3 to vertex 8, and from vertex 5 to verte... | 4 | MATH |
[
{
"content": "Suppose you have a 7-gon, with vertices numbered 1 through 7 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 7, from vertex 5 to vertex 2, from vertex 6 to vertex 2, from vertex 4 to vertex 2, from vertex 4 to vertex 6, and from vertex 4 to vertex 7. How many distinct pairs of... | 0 | 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 3, from vertex 1 to vertex 5, from vertex 6 to vertex 3, from vertex 6 to vertex 4, from vertex 1 to vertex 4, from vertex 6 to vertex 2, and from vertex 4 to vertex 2.... | 4 | MATH |
[
{
"content": "Suppose you have a 14-gon, with vertices numbered 1 through 14 in counterclockwise order. Draw the diagonal from vertex 8 to vertex 10, from vertex 12 to vertex 4, from vertex 6 to vertex 3, from vertex 7 to vertex 13, from vertex 4 to vertex 14, from vertex 9 to vertex 14, and from vertex 5 to ve... | 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 5, from vertex 6 to vertex 3, from vertex 6 to vertex 2, from vertex 1 to vertex 4, from vertex 6 to vertex 4, and from vertex 2 to vertex 4. 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 2 to vertex 8, from vertex 1 to vertex 3, from vertex 2 to vertex 7, from vertex 6 to vertex 8, from vertex 5 to vertex 8, and from vertex 7 to vertex 5. How many distinct pairs of... | 2 | MATH |
[
{
"content": "Suppose you have a 15-gon, with vertices numbered 1 through 15 in counterclockwise order. Draw the diagonal from vertex 3 to vertex 6, from vertex 7 to vertex 12, from vertex 14 to vertex 2, from vertex 15 to vertex 6, from vertex 9 to vertex 5, from vertex 15 to vertex 7, and from vertex 6 to ver... | 0 | 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 3, from vertex 3 to vertex 10, from vertex 2 to vertex 5, from vertex 4 to vertex 8, from vertex 11 to vertex 3, and from vertex 10 to vertex 2. How many distinct pai... | 1 | 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 7, from vertex 3 to vertex 8, from vertex 1 to vertex 8, from vertex 8 to vertex 5, from vertex 11 to vertex 7, from vertex 10 to vertex 7, and from vertex 9 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 5 to vertex 3, from vertex 4 to vertex 1, from vertex 5 to vertex 9, from vertex 1 to vertex 12, from vertex 13 to vertex 11, from vertex 7 to vertex 3, and from vertex 13 to ver... | 1 | 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 1, from vertex 11 to vertex 5, from vertex 7 to vertex 4, from vertex 9 to vertex 12, from vertex 12 to vertex 8, from vertex 6 to vertex 10, and from vertex 6 to ver... | 0 | 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 2, from vertex 2 to vertex 7, from vertex 5 to vertex 1, from vertex 7 to vertex 5, from vertex 10 to vertex 4, and from vertex 5 to vertex 10. How many distinct pair... | 2 | 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 4, from vertex 1 to vertex 5, from vertex 6 to vertex 4, from vertex 4 to vertex 2, from vertex 2 to vertex 5, from vertex 2 to vertex 6, and from vertex 3 to vertex 6.... | 4 | 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 1, from vertex 1 to vertex 3, from vertex 1 to vertex 6, from vertex 1 to vertex 11, from vertex 5 to vertex 8, from vertex 8 to vertex 2, and from vertex 9 to verte... | 3 | 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 2, from vertex 2 to vertex 8, from vertex 10 to vertex 6, from vertex 5 to vertex 2, from vertex 6 to vertex 8, and from vertex 9 to vertex 3. How many distinct pairs... | 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 3, from vertex 9 to vertex 3, from vertex 2 to vertex 9, from vertex 8 to vertex 2, from vertex 4 to vertex 6, from vertex 4 to vertex 10, and from vertex 8 to vertex... | 0 | 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 2, from vertex 1 to vertex 9, from vertex 14 to vertex 9, from vertex 5 to vertex 1, from vertex 5 to vertex 13, from vertex 3 to vertex 8, and from vertex 6 to verte... | 2 | 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 8, from vertex 1 to vertex 10, from vertex 11 to vertex 6, from vertex 11 to vertex 9, from vertex 12 to vertex 6, from vertex 7 to vertex 2, 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 8 to vertex 5, from vertex 11 to vertex 8, from vertex 9 to vertex 2, from vertex 6 to vertex 4, from vertex 9 to vertex 4, and from vertex 5 to vertex 7. How many distinct pairs... | 2 | MATH |
[
{
"content": "Suppose you have a 15-gon, with vertices numbered 1 through 15 in counterclockwise order. Draw the diagonal from vertex 6 to vertex 3, from vertex 10 to vertex 12, from vertex 15 to vertex 4, from vertex 6 to vertex 11, from vertex 9 to vertex 13, and from vertex 13 to vertex 4. How many distinct ... | 0 | 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 10, from vertex 8 to vertex 4, from vertex 8 to vertex 10, from vertex 5 to vertex 2, from vertex 2 to vertex 9, and from vertex 11 to vertex 3. 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 4 to vertex 1, from vertex 2 to vertex 5, from vertex 3 to vertex 5, from vertex 2 to vertex 6, from vertex 5 to vertex 1, and from vertex 2 to vertex 4. How many distinct pairs of... | 2 | 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 1 to vertex 5, from vertex 6 to vertex 2, from vertex 7 to vertex 5, from vertex 7 to vertex 4, and from vertex 4 to vertex 6. How many distinct pairs of... | 2 | 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 3 to vertex 8, from vertex 7 to vertex 3, from vertex 7 to vertex 4, from vertex 8 to vertex 4, from vertex 1 to vertex 6, and from vertex 4 to vertex 2.... | 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 3, from vertex 1 to vertex 3, from vertex 2 to vertex 7, from vertex 4 to vertex 7, from vertex 8 to vertex 10, and from vertex 5 to vertex 1. How many distinct pairs... | 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 11, from vertex 9 to vertex 1, from vertex 7 to vertex 14, from vertex 7 to vertex 10, from vertex 12 to vertex 6, and from vertex 10 to vertex 8. How many distinct ... | 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 3, from vertex 2 to vertex 11, from vertex 5 to vertex 1, from vertex 10 to vertex 5, from vertex 8 to vertex 1, and from vertex 10 to vertex 2. How many distinct pai... | 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 4, from vertex 9 to vertex 7, from vertex 3 to vertex 1, from vertex 10 to vertex 7, from vertex 10 to vertex 2, and from vertex 3 to vertex 10. How many distinct pai... | 1 | 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 4, from vertex 3 to vertex 1, from vertex 6 to vertex 8, from vertex 3 to vertex 6, from vertex 5 to vertex 1, from vertex 6 to vertex 4, and from vertex 3 to vertex 8.... | 2 | 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 7, from vertex 1 to vertex 10, from vertex 2 to vertex 4, from vertex 6 to vertex 2, from vertex 13 to vertex 3, from vertex 14 to vertex 12, and from vertex 1 to ver... | 0 | 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 2, from vertex 3 to vertex 7, from vertex 1 to vertex 6, from vertex 5 to vertex 8, from vertex 12 to vertex 5, and from vertex 9 to vertex 7. How many distinct pair... | 2 | 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 3 to vertex 1, from vertex 1 to vertex 4, from vertex 6 to vertex 3, from vertex 2 to vertex 5, and from vertex 3 to vertex 5. How many distinct pairs of... | 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 5 to vertex 2, from vertex 5 to vertex 1, from vertex 2 to vertex 6, from vertex 2 to vertex 4, and from vertex 4 to vertex 1. How many distinct pairs of... | 2 | MATH |
[
{
"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 8 to vertex 2, from vertex 4 to vertex 7, from vertex 7 to vertex 3, from vertex 5 to vertex 3, from vertex 6 to vertex 8, and from vertex 2 to vertex 6.... | 4 | MATH |
[
{
"content": "Suppose you have a 15-gon, with vertices numbered 1 through 15 in counterclockwise order. Draw the diagonal from vertex 12 to vertex 7, from vertex 14 to vertex 4, from vertex 6 to vertex 13, from vertex 7 to vertex 13, from vertex 11 to vertex 15, from vertex 13 to vertex 10, and from vertex 10 t... | 0 | 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 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 6-gon, with vertices numbered 1 through 6 in counterclockwise order. Draw the diagonal from vertex 4 to vertex 6, from vertex 3 to vertex 5, from vertex 6 to vertex 2, from vertex 3 to vertex 1, from vertex 2 to vertex 4, from vertex 6 to vertex 3, and from vertex 1 to vertex 5.... | 2 | 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 11, from vertex 4 to vertex 1, from vertex 8 to vertex 2, from vertex 12 to vertex 7, from vertex 14 to vertex 8, and from vertex 13 to vertex 10. How many distinct p... | 0 | 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 12, from vertex 7 to vertex 13, from vertex 9 to vertex 6, from vertex 11 to vertex 14, from vertex 2 to vertex 8, from vertex 13 to vertex 10, and from vertex 8 to v... | 0 | 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 11, from vertex 8 to vertex 10, from vertex 1 to vertex 4, from vertex 10 to vertex 7, from vertex 5 to vertex 9, from vertex 2 to vertex 12, and from vertex 11 to ve... | 0 | 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 7, from vertex 4 to vertex 10, from vertex 4 to vertex 1, from vertex 1 to vertex 7, from vertex 10 to vertex 3, and from vertex 6 to vertex 9. How many distinct pair... | 3 | MATH |
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