You can navigate the grid below from the top-left yellow circle to the bottom-right yellow square by making only orthogonal (not diagonal) moves, going from one position to the next only if the shape and/or the color of the shape in the entered cell is the same as that of the cell you are leaving.

• What path has the minimum number of moves without going through the same cell twice?
• What path has the maximum number of moves without going through the same cell twice?

(In reply to Best Minimum? by Jim Keneipp)

unfortunately your path fails on the second move when you move from a yellow circle to a blue square.  Niether the shape nor the color match, thus this move can not be made.

Posted by Daniel on 2009-10-07 14:28:35