id stringlengths 19 40 | setting_key stringclasses 16
values | messages listlengths 1 1 | ground_truth stringlengths 1 8 | dataset stringclasses 2
values | setting_name stringclasses 7
values | prompt stringlengths 177 3.21k |
|---|---|---|---|---|---|---|
geometry_polygon_color_test_out_013 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, ... | 4 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 10 is red. How many valid colorings... |
geometry_polygon_color_test_out_014 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximum... | 4 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximum number of blue vertices that can be made ... |
geometry_polygon_color_test_out_015 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is blue, v... | 1 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is blue, vertex 10 is red. How many valid colorings ... |
geometry_polygon_color_test_out_016 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blu... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maximum number of blue vert... |
geometry_polygon_color_test_out_017 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. Ho... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colorings of the uncolored ve... |
geometry_polygon_color_test_out_018 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. ... | 4 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maximum number of red vertices... |
geometry_polygon_color_test_out_019 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is red... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is red. What is the maximum number of blue verti... |
geometry_polygon_color_test_out_020 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. The 10-gon is the... | 2 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. The 10-gon is then rotated clockwise by 7 positions, so tha... |
geometry_polygon_color_test_out_021 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is blue... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is blue. The 11-gon is then rotated clockwise by ... |
geometry_polygon_color_test_out_022 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximu... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue vertices that can be made... |
geometry_polygon_color_test_out_023 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is uncolored, vertex 5 is uncolored, vertex 6 is uncolored, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. ... | 0 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is uncolored, vertex 5 is uncolored, vertex 6 is uncolored, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. How many valid colorings of the uncolored ... |
geometry_polygon_color_test_out_024 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is uncolored, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is red. H... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is uncolored, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is red. How many valid colorings of the uncolored v... |
geometry_polygon_color_test_out_025 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is red, ver... | 6 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is red, vertex 10 is blue. How many valid colorings o... |
geometry_polygon_color_test_out_026 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maximu... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue vertices that can be made... |
geometry_polygon_color_test_out_027 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximu... | 4 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue vertices that can be made... |
geometry_polygon_color_test_out_028 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is uncolored, vertex 9 is uncolored, vertex... | 0 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is uncolored, vertex 9 is uncolored, vertex 10 is uncolored. How many valid colorings... |
geometry_polygon_color_test_out_029 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex... | 5 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is uncolored, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is red, vertex 10 is uncolored. How many valid colorings... |
geometry_polygon_color_test_out_030 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is red, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is uncolored, vertex 9 is blue.... | 0 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is red, vertex 2 is uncolored, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is uncolored, vertex 9 is blue. How many valid colorings of the uncolored... |
geometry_polygon_color_test_out_031 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is uncolored, ve... | 2 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is uncolored, vertex 10 is blue. How many valid colorings ... |
geometry_polygon_color_test_out_032 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum n... | 2 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is red, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum number of blue vertices that can be made to... |
geometry_polygon_color_test_out_033 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is red. What is the maximu... | 5 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is red. What is the maximum number of red vertices that can be made ... |
geometry_polygon_color_test_out_034 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue... | 4 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximum number of red vertic... |
geometry_polygon_color_test_out_035 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is uncolored, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is blue. H... | 2 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is uncolored, vertex 4 is uncolored, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is blue. How many valid colorings of the uncolored v... |
geometry_polygon_color_test_out_036 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 1... | 0 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is red, vertex 8 is uncolored, vertex 9 is red, vertex 10 is uncolored. How many valid colorings o... |
geometry_polygon_color_test_out_037 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximu... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is red, vertex 9 is blue. What is the maximum number of red vertices that can be made ... |
geometry_polygon_color_test_out_038 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maxi... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue. What is the maximum number of blue vertices that can be ma... |
geometry_polygon_color_test_out_039 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue. What is the maxim... | 4 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is red, vertex 6 is blue, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue. What is the maximum number of blue vertices that can be mad... |
geometry_polygon_color_test_out_040 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue, vertex 10 is red.... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is red, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is blue, vertex 9 is blue, vertex 10 is red. What is the maximum number of blue vertic... |
geometry_polygon_color_test_out_041 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is blue, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximum number of red vertic... |
geometry_polygon_color_test_out_042 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is blue. Ho... | 3 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is uncolored, vertex 3 is red, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is uncolored, vertex 9 is blue. How many valid colorings of the uncolored ve... |
geometry_polygon_color_test_out_043 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue... | 3 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue, vertex 10 is blue. What is the maximum number of blue verti... |
geometry_polygon_color_test_out_044 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum... | 4 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is blue, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is red. What is the maximum number of blue vertices that can be made ... |
geometry_polygon_color_test_out_045 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blue... | 4 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is blue, vertex 3 is blue, vertex 4 is red, vertex 5 is blue, vertex 6 is blue, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is blue. What is the maximum number of red vertic... |
geometry_polygon_color_test_out_046 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is red, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. H... | 1 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is blue, vertex 1 is red, vertex 2 is blue, vertex 3 is uncolored, vertex 4 is red, vertex 5 is uncolored, vertex 6 is blue, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colorings of the uncolored v... |
geometry_polygon_color_test_out_047 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximu... | 4 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is red, vertex 8 is blue, vertex 9 is blue. What is the maximum number of red vertices that can be made ... |
geometry_polygon_color_test_out_048 | geometry_polygon_color | [
{
"role": "user",
"content": "A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is red. ... | 4 | MATH_EXPLORATIVE | null | A 11-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is red, vertex 1 is red, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is blue, vertex 6 is red, vertex 7 is blue, vertex 8 is red, vertex 9 is blue, vertex 10 is red. What is the maximum number of red vertices... |
geometry_polygon_color_test_out_049 | geometry_polygon_color | [
{
"role": "user",
"content": "A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is uncolored, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. Ho... | 2 | MATH_EXPLORATIVE | null | A 10-gon is colored so that in clockwise order, the vertices are colored as follows: vertex 0 is uncolored, vertex 1 is uncolored, vertex 2 is red, vertex 3 is blue, vertex 4 is blue, vertex 5 is red, vertex 6 is red, vertex 7 is uncolored, vertex 8 is blue, vertex 9 is red. How many valid colorings of the uncolored ve... |
logic_gridworld_blocked_test_out_000 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (5, 8), (2, 8), (1, 2), (9, 6), (6, 8), (8,... | 876 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (5, 8), (2, 8), (1, 2), (9, 6), (6, 8), (8, 0), (8, 1), (9, 7), (6, 4), (7, 7), (9, 1... |
logic_gridworld_blocked_test_out_001 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (3, 5), (0, 3), (3, 4), (2, 1), (7, 0)?\n\nP... | 470 | MATH_EXPLORATIVE | null | In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (3, 5), (0, 3), (3, 4), (2, 1), (7, 0)?
Present the answer in LaTex format: \boxed{Yo... |
logic_gridworld_blocked_test_out_002 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (7, 3), (6, 2), (0, 3), (1, 1)?\n\nPresent t... | 486 | MATH_EXPLORATIVE | null | In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (7, 3), (6, 2), (0, 3), (1, 1)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_003 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 0), (2, 3), (1, 6), (0, 3), (6, 0), (2,... | 288 | MATH_EXPLORATIVE | null | In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 3), (4, 0), (2, 3), (1, 6), (0, 3), (6, 0), (2, 2), (1, 4), (5, 1), (0, 8)?
Present the ... |
logic_gridworld_blocked_test_out_004 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (3, 8), (6, 8), (5, 1), (1, 8), (0, 9), (6,... | 1612 | MATH_EXPLORATIVE | null | In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 3), (3, 8), (6, 8), (5, 1), (1, 8), (0, 9), (6, 6), (3, 1), (5, 6)?
Present the answer i... |
logic_gridworld_blocked_test_out_005 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 3), (1, 3), (4, 5), (6, 5), (5, 4), (1, ... | 0 | MATH_EXPLORATIVE | null | In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (2, 3), (1, 3), (4, 5), (6, 5), (5, 4), (1, 1), (4, 6)?
Present the answer in LaTex f... |
logic_gridworld_blocked_test_out_006 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (1, 1), (5, 0), (4, 2), (3, 6)?\n\nPresent t... | 134 | MATH_EXPLORATIVE | null | In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (1, 1), (5, 0), (4, 2), (3, 6)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_007 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (6, 3), (2, 6), (2, 1), (0, 5), (1, 4), (0,... | 0 | MATH_EXPLORATIVE | null | In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 6), (6, 3), (2, 6), (2, 1), (0, 5), (1, 4), (0, 3), (2, 0), (8, 7), (8, 4), (0, 1), (5, 1... |
logic_gridworld_blocked_test_out_008 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (9, 5), (5, 2), (7, 2), (6, 0), (5, 4), (4,... | 5232 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (9, 5), (5, 2), (7, 2), (6, 0), (5, 4), (4, 4), (6, 4)?
Present the answer in LaTex ... |
logic_gridworld_blocked_test_out_009 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (1, 5), (0, 5)?\n\nPresent the answer in LaT... | 12105 | MATH_EXPLORATIVE | null | In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 6), (1, 5), (0, 5)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_010 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (5, 4), (4, 3), (2, 0), (8, 5), (8, 0), (6,... | 21 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (5, 4), (4, 3), (2, 0), (8, 5), (8, 0), (6, 6), (4, 4), (5, 3), (4, 5), (1, 0), (9, 2... |
logic_gridworld_blocked_test_out_011 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 6), (0, 5), (7, 4), (6, 1), (6, 6), (1,... | 210 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (3, 6), (0, 5), (7, 4), (6, 1), (6, 6), (1, 1), (0, 4), (6, 3), (8, 5)?
Present the ... |
logic_gridworld_blocked_test_out_012 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (7, 3), (6, 7), (3, 0), (7, 1), (7, 4), (6,... | 1622 | MATH_EXPLORATIVE | null | In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 6), (7, 3), (6, 7), (3, 0), (7, 1), (7, 4), (6, 3), (6, 8), (2, 0), (3, 8), (3, 4)?
Pres... |
logic_gridworld_blocked_test_out_013 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 0), (4, 0)?\n\nPresent the answer in LaTex forma... | 3312 | MATH_EXPLORATIVE | null | In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 0), (4, 0)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_014 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (4, 4), (4, 7), (9, 0), (7, 3), (8, 5), (3,... | 2560 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (4, 4), (4, 7), (9, 0), (7, 3), (8, 5), (3, 1), (1, 7), (0, 7), (7, 1), (4, 6), (0, 6... |
logic_gridworld_blocked_test_out_015 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 0), (5, 6)?\n\nPresent the answer in LaT... | 1681 | MATH_EXPLORATIVE | null | In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 0), (5, 6)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_016 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (7, 1), (4, 2)?\n\nPresent the answer in LaT... | 1083 | MATH_EXPLORATIVE | null | In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (7, 1), (4, 2)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_017 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (6, 1), (1, 8), (5, 6), (3, 2), (9, 2)?\n\n... | 7390 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 2), (6, 1), (1, 8), (5, 6), (3, 2), (9, 2)?
Present the answer in LaTex format: \boxed{Y... |
logic_gridworld_blocked_test_out_018 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 4), (2, 5), (3, 7), (2, 3), (3, 3)?\n\nP... | 183 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (3, 4), (2, 5), (3, 7), (2, 3), (3, 3)?
Present the answer in LaTex format: \boxed{Yo... |
logic_gridworld_blocked_test_out_019 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (6, 5), (2, 1), (7, 2), (4, 1), (4, 5), (3, ... | 380 | MATH_EXPLORATIVE | null | In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (6, 5), (2, 1), (7, 2), (4, 1), (4, 5), (3, 2), (2, 8), (4, 4), (3, 4), (0, 5), (1, 0)... |
logic_gridworld_blocked_test_out_020 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (5, 6), (3, 4), (1, 4), (5, 5)?\n\nPresent t... | 175 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 7), (5, 6), (3, 4), (1, 4), (5, 5)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_021 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (5, 9), (6, 3), (6, 0), (3, 0), (1, 7), (6,... | 6309 | MATH_EXPLORATIVE | null | In a 8x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (5, 9), (6, 3), (6, 0), (3, 0), (1, 7), (6, 5)?
Present the answer in LaTex format: ... |
logic_gridworld_blocked_test_out_022 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (7, 0), (9, 2), (5, 2), (8, 3), (2, 5), (8,... | 966 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 6), (7, 0), (9, 2), (5, 2), (8, 3), (2, 5), (8, 6)?
Present the answer in LaTex format: ... |
logic_gridworld_blocked_test_out_023 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 6), (4, 5), (1, 5), (4, 2), (5, 5), (6, ... | 90 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (0, 6), (4, 5), (1, 5), (4, 2), (5, 5), (6, 2), (2, 1), (3, 5), (3, 0)?
Present the a... |
logic_gridworld_blocked_test_out_024 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (6, 0), (8, 3), (3, 7), (5, 6), (2, 5), (7,... | 414 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 5), (6, 0), (8, 3), (3, 7), (5, 6), (2, 5), (7, 6), (8, 7), (3, 3), (7, 1), (1, 3), (1, 0... |
logic_gridworld_blocked_test_out_025 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (8, 7), (6, 3), (0, 7), (5, 8), (7, 3), (1, ... | 581 | MATH_EXPLORATIVE | null | In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 8), (8, 7), (6, 3), (0, 7), (5, 8), (7, 3), (1, 4), (8, 6), (1, 1), (6, 6), (8, 0), (7, 2)... |
logic_gridworld_blocked_test_out_026 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (5, 3), (4, 0), (8, 2), (8, 3), (4, 3), (3,... | 1119 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (5, 3), (4, 0), (8, 2), (8, 3), (4, 3), (3, 5)?
Present the answer in LaTex format: ... |
logic_gridworld_blocked_test_out_027 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (5, 6), (3, 4), (0, 5), (2, 6)?\n\nPresent t... | 149 | MATH_EXPLORATIVE | null | In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (5, 6), (3, 4), (0, 5), (2, 6)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_028 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (0, 8), (7, 2), (4, 4), (4, 7), (6, 6), (1, ... | 649 | MATH_EXPLORATIVE | null | In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 4), (0, 8), (7, 2), (4, 4), (4, 7), (6, 6), (1, 5), (6, 2), (0, 7), (5, 3)?
Present the a... |
logic_gridworld_blocked_test_out_029 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 7), (6, 7), (2, 6), (0, 5), (2, 7), (7, ... | 1236 | MATH_EXPLORATIVE | null | In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (0, 7), (6, 7), (2, 6), (0, 5), (2, 7), (7, 3), (8, 4), (3, 7), (6, 2), (1, 4), (0, 2)... |
logic_gridworld_blocked_test_out_030 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (8, 5), (1, 4), (7, 8), (7, 0), (6, 1), (2, ... | 976 | MATH_EXPLORATIVE | null | In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (8, 5), (1, 4), (7, 8), (7, 0), (6, 1), (2, 5), (5, 5), (2, 8), (3, 0), (3, 7), (6, 0)... |
logic_gridworld_blocked_test_out_031 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (5, 1), (3, 3), (1, 3), (4, 2), (2, 0), (7, ... | 0 | MATH_EXPLORATIVE | null | In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (5, 1), (3, 3), (1, 3), (4, 2), (2, 0), (7, 5), (7, 7), (3, 2), (6, 5), (0, 3)?
Prese... |
logic_gridworld_blocked_test_out_032 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (6, 2), (0, 4), (6, 1), (5, 2), (2, 4)?\n\nP... | 3009 | MATH_EXPLORATIVE | null | In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (6, 2), (0, 4), (6, 1), (5, 2), (2, 4)?
Present the answer in LaTex format: \boxed{Yo... |
logic_gridworld_blocked_test_out_033 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (5, 6), (6, 2), (3, 1), (5, 2), (2, 3), (1, ... | 230 | MATH_EXPLORATIVE | null | In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (5, 6), (6, 2), (3, 1), (5, 2), (2, 3), (1, 7), (1, 8), (1, 4), (1, 1)?
Present the a... |
logic_gridworld_blocked_test_out_034 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (8, 3), (8, 2)?\n\nPresent the answer in LaT... | 2793 | MATH_EXPLORATIVE | null | In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 4), (8, 3), (8, 2)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_035 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (3, 8), (6, 2), (8, 0), (7, 3), (1, 1)?\n\n... | 6556 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (3, 8), (6, 2), (8, 0), (7, 3), (1, 1)?
Present the answer in LaTex format: \boxed{Y... |
logic_gridworld_blocked_test_out_036 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (2, 1), (5, 6), (0, 1)?\n\nPresent the answe... | 212 | MATH_EXPLORATIVE | null | In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 5), (2, 1), (5, 6), (0, 1)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_037 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (5, 8), (6, 0), (3, 6), (3, 3), (6, 4), (5,... | 2472 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (5, 8), (6, 0), (3, 6), (3, 3), (6, 4), (5, 4), (3, 4), (8, 8)?
Present the answer i... |
logic_gridworld_blocked_test_out_038 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 0), (7, 3), (4, 0), (2, 5), (2, 0), (3, ... | 222 | MATH_EXPLORATIVE | null | In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (3, 0), (7, 3), (4, 0), (2, 5), (2, 0), (3, 4), (1, 4), (3, 3), (7, 4), (0, 4)?
Prese... |
logic_gridworld_blocked_test_out_039 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 4), (0, 3), (0, 1), (7, 6), (9, 2)?\n\n... | 1153 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (3, 4), (0, 3), (0, 1), (7, 6), (9, 2)?
Present the answer in LaTex format: \boxed{Y... |
logic_gridworld_blocked_test_out_040 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 4), (3, 2), (5, 1)?\n\nPresent the answe... | 900 | MATH_EXPLORATIVE | null | In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 7), (3, 4), (3, 2), (5, 1)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_041 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (4, 9), (2, 7), (3, 3), (2, 4), (0, 9), (3,... | 1188 | MATH_EXPLORATIVE | null | In a 9x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (4, 9), (2, 7), (3, 3), (2, 4), (0, 9), (3, 7), (5, 4), (3, 1), (7, 7), (8, 0)?
Pres... |
logic_gridworld_blocked_test_out_042 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 8), (4, 2)?\n\nPresent the answer in LaT... | 2378 | MATH_EXPLORATIVE | null | In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (3, 8), (4, 2)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_043 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (2, 3), (6, 2), (1, 2)?\n\nPresent the answe... | 2472 | MATH_EXPLORATIVE | null | In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (2, 3), (6, 2), (1, 2)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_044 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (2, 4), (6, 2), (3, 6)?\n\nPresent the answe... | 1431 | MATH_EXPLORATIVE | null | In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 4), (2, 4), (6, 2), (3, 6)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_045 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (0, 2), (3, 5), (4, 3), (6, 1), (7, 3), (0, ... | 1162 | MATH_EXPLORATIVE | null | In a 8x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 5), (0, 2), (3, 5), (4, 3), (6, 1), (7, 3), (0, 3)?
Present the answer in LaTex format: \... |
logic_gridworld_blocked_test_out_046 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (6, 2), (3, 1), (7, 6), (3, 2)?\n\nPresent t... | 828 | MATH_EXPLORATIVE | null | In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (6, 2), (3, 1), (7, 6), (3, 2)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_047 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (4, 5), (6, 6), (3, 6), (3, 1), (5, 2), (1, ... | 122 | MATH_EXPLORATIVE | null | In a 7x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 3), (4, 5), (6, 6), (3, 6), (3, 1), (5, 2), (1, 2)?
Present the answer in LaTex format: \... |
logic_gridworld_blocked_test_out_048 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 3), (5, 5), (0, 2), (4, 0), (3, 6)?\n\nP... | 108 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 0), (4, 3), (5, 5), (0, 2), (4, 0), (3, 6)?
Present the answer in LaTex format: \boxed{Yo... |
logic_gridworld_blocked_test_out_049 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (4, 6), (5, 3), (1, 5), (4, 0), (6, 2), (4, ... | 649 | MATH_EXPLORATIVE | null | In a 8x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (4, 6), (5, 3), (1, 5), (4, 0), (6, 2), (4, 2)?
Present the answer in LaTex format: \... |
logic_gridworld_blocked_test_out_050 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (6, 2)?\n\nPresent the answer in LaTex forma... | 3327 | MATH_EXPLORATIVE | null | In a 9x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 5), (6, 2)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_051 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (0, 2), (6, 1), (0, 8), (3, 8), (1, 0), (8, ... | 2930 | MATH_EXPLORATIVE | null | In a 9x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 6), (0, 2), (6, 1), (0, 8), (3, 8), (1, 0), (8, 1), (1, 6)?
Present the answer in LaTex f... |
logic_gridworld_blocked_test_out_052 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (7, 8), (5, 3), (5, 1), (0, 7), (3, 0), (7,... | 3336 | MATH_EXPLORATIVE | null | In a 10x9 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 8), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (7, 8), (5, 3), (5, 1), (0, 7), (3, 0), (7, 1), (8, 0), (4, 5)?
Present the answer i... |
logic_gridworld_blocked_test_out_053 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (8, 3), (2, 4), (9, 3), (5, 2)?\n\nPresent ... | 6555 | MATH_EXPLORATIVE | null | In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 2), (8, 3), (2, 4), (9, 3), (5, 2)?
Present the answer in LaTex format: \boxed{Your answ... |
logic_gridworld_blocked_test_out_054 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (5, 4), (6, 2), (2, 5), (2, 7)?\n\nPresent t... | 854 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 0), (5, 4), (6, 2), (2, 5), (2, 7)?
Present the answer in LaTex format: \boxed{Your answe... |
logic_gridworld_blocked_test_out_055 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 1), (4, 3), (2, 3), (4, 0), (5, 3), (2, ... | 27 | MATH_EXPLORATIVE | null | In a 7x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (0, 1), (4, 3), (2, 3), (4, 0), (5, 3), (2, 0), (5, 5), (5, 1)?
Present the answer in... |
logic_gridworld_blocked_test_out_056 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (2, 5)?\n\nPresent the answer in LaTex form... | 4445 | MATH_EXPLORATIVE | null | In a 10x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 1), (2, 5)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_057 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 0)?\n\nPresent the answer in LaTex forma... | 783 | MATH_EXPLORATIVE | null | In a 9x7 grid, how many different paths are there from the bottom left (0, 0) to the top right (8, 6), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (1, 0)?
Present the answer in LaTex format: \boxed{Your answer} |
logic_gridworld_blocked_test_out_058 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (5, 3), (1, 7), (9, 7), (2, 0), (7, 8), (3... | 427 | MATH_EXPLORATIVE | null | In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (5, 3), (1, 7), (9, 7), (2, 0), (7, 8), (3, 6), (1, 0), (0, 9), (2, 7), (2, 9), (0, ... |
logic_gridworld_blocked_test_out_059 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (6, 4), (2, 6), (3, 1), (0, 2), (4, 4)?\n\n... | 522 | MATH_EXPLORATIVE | null | In a 7x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 3), (6, 4), (2, 6), (3, 1), (0, 2), (4, 4)?
Present the answer in LaTex format: \boxed{Y... |
logic_gridworld_blocked_test_out_060 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 2), (7, 1), (2, 5), (5, 2), (7, 5), (2, ... | 259 | MATH_EXPLORATIVE | null | In a 8x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (7, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 0), (2, 2), (7, 1), (2, 5), (5, 2), (7, 5), (2, 4), (3, 0), (1, 0), (3, 5)?
Present the a... |
logic_gridworld_blocked_test_out_061 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (6, 1), (7, 2), (0, 2), (9, 4), (1, 1), (9,... | 192 | MATH_EXPLORATIVE | null | In a 10x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (6, 1), (7, 2), (0, 2), (9, 4), (1, 1), (9, 5), (6, 5), (3, 6), (4, 3), (5, 7), (5, 0... |
logic_gridworld_blocked_test_out_062 | logic_gridworld_blocked | [
{
"role": "user",
"content": "In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 4), (0, 3), (0, 7), (4, 1), (1, 3), (5, ... | 367 | MATH_EXPLORATIVE | null | In a 7x8 grid, how many different paths are there from the bottom left (0, 0) to the top right (6, 7), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 4), (1, 4), (0, 3), (0, 7), (4, 1), (1, 3), (5, 5)?
Present the answer in LaTex format: \... |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 21