two comments...

dynamic 2009-04-25 02:48:44 ( reads)

1. the proof of claim 2 is correct but incomplete. the border grids need to be discussed separately.

2. the construction only works for n mod 4 = 1. If n mod 4 = 3, then the number of red grids in claim 2 and 3 are the same. let me think what to do in this case...