Discrete Mathematics 47

tiles, the problematic green tile will prevent the light and dark squares from balancing. So

there can be no tiling.

5.4 Escape!

Consider next the game Escape! We have three stones in the corner of an infinite quarter

plane of squares. The rule of movement is that you can select any stone you like, and it

will split into two stones, one moving to the square above and one moving to the square to

the right of where it had been. The move is allowed only when both of those squares are

empty, so that they may accept the new stones. The goal is to vacate the shaded L-shaped

region at the origin.

Can you vacate the shaded corner area? Please give it a try. One can make a good

start, but then the outer stones begin to block one’s path. You have to move these other

stones out of the way to make room. Is it possible to get all three stones out of the

corner? I have provided an online interactive version of the game, for trying out strate-

gies and ideas, at https://scratch.mit.edu/projects/195391196, and see also my blog post at

http://jdh.hamkins.org/escape.

Interlude. . .