17×17: Some Attempts at Doubly-Symmetrical Rotations
9/04/2010Note: this is part of a series of posts is related to the “17×17 Challenge” posted by Bill Gasarch. The goal is to color cells of a 17 by 17 grid, using only four colors, such that no rectangle is formed from four cells of the same color.
In a previous post I presented rotations of some single-color rectangle-free grids which were symmetrical along a diagonal axis. I also noticed that, of the single-colorings of optimal size which I could generate, all with an odd number side-length could be made symmetrical along both diagonals (the evens could not):
Perhaps all odd-sided optimal single-colorings are doubly-symmetrical in one of their rotations! That would be a cool thing to learn, and it would also mean that if we wanted to generate an optimal coloring, then our search space would be roughly 1/4 of the grid.