In attempting (and failing) to solve the puzzle when it first came out, I noticed that there were quite a few ways to colour the squares/place the kings for each minimum solution, some quite symmetrical and interesting. I wondered how many such "colourings" existed for each size of grid. And so because I apparently had nothing better to do over the weekend, I invested an inordinate amount of time coding up a script to bruteforce the number of colourings, and then a similarly inordinate amount of time optimizing it so I could get past a 5x5 grid. Here are the results:
2x2: 6
3x3: 2
4x4: 1296
5x5: 371
6x6: 8
Haven't been able to go any farther with my current script, but for what it's worth, here it is on GitHub.
2x2: 6
3x3: 2
4x4: 1296
5x5: 371
6x6: 8
Haven't been able to go any farther with my current script, but for what it's worth, here it is on GitHub.
on /blog/114