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Note that the second distinction you made is actually trivial. Coloring the vertices of a planar graph is the same problem as coloring the regions of a different planar graph. The graphs are duals:

http://en.wikipedia.org/wiki/Dual_graph

In this case, the dual of a grid is a grid. So at least that part of it would be the same problem. The other distinctions are true, though.



Of course you are right. I guess I pictured the 17x17=289 points forming 16x16=256 squares, which is why I felt it necessary to make the distinction.




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