Excellent, thank you. I shall ignore the fact that there will be other sized grids that are looking for solutions.
Still, it's always interesting to see if one can develop something to come up with one's own solution.
Still, it's always interesting to see if one can develop something to come up with one's own solution.
Nope! We now know for all grid sizes whether or not they are rectangle-free four-colorable. 17x17, 17x18, and 18x18 were the last remaining cases (there are no such grids larger than 18x18). So you have nothing to worry about.
Sounds like a challenge :-) Seriously though, I am not a mathematician, did the SAT solution to the 17 x 17 show there were no solutions past 18 x 18? I ask because on the original challenge site was an update [1] which I was trying to parse. It talks about OBS4 but I was trying to parse if that was the class of problem or the particular challenge problem.
[1] "UPDATE: THE RESULTS ABOUT OBS4 HAVE CHANGED SINCE THE ORIGINAL POST SINCE BRAD LARSON EMAILED ME A 4-COL OF 21x10 and 21x11. UPDATE: BRAD LARSON EMAILED ME A 4-COL OF 22x10. " -- http://blog.computationalcomplexity.org/2009/11/17x17-challe...