+88 Given a 3 x 5 grid, where point A is the lower left corner and B is the upper right corner, how many ways can a spider travel on the grid, given that it can travel one unit right, up, or down each move and cannot revisit an edge or vertex?
I know that to count for paths where the spider can only move up and right (for example), the answer would be \({5 + 3} \choose 5\), which is 56. However, how do I account for moving both up or down? Since the spider can move up or down, would there be 3*2 choices to move vertically? Then the answer might be \({5 + 6} \choose 5\)= 462.
Is my logic correct?
