fragmentary ideas ䷿ intellectual what-nots ䷷ and haskell programming ䷴

Note: 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 my last post I noticed that all of the smaller optimal single-colorings I generated showed diagonal symmetry, meaning that row 1 is the same as column 1, row 8 is the same as column 8, etc. It’s my hypothesis that all complete single-colorings are symmetrical in this way.

I decided to play with making the known 74-cell subset symmetrical by applying rotations and came up with this:

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