messages
listlengths
1
1
ground_truth
stringclasses
7 values
dataset
stringclasses
1 value
[ { "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