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.
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What path has the minimum number of moves without going through the same cell twice?
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What path has the maximum number of moves without going through the same cell twice?
(In reply to
re: Best Minimum? by Daniel)
I think this was my original solution, although looking back on it there is an initial "D-" hanging on a line above the rest of the sequence that would be easy to miss -- guess I should have put it all on its own line. But nonetheless I think we have the best minimum so far, and as far as I can tell you have the best maximum (so far).