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How many knights can you fit on a chess board without any being threatened?

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12
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32 knights: all on white or all on black. When a knight moves, it moves to a space of a different color. If they are all on the same color, no collision happens.

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  • $\begingroup$ If there were required to be equal numbers of black and white knights, and knights only threatened the opposite color, what would the answer be? Placing 48 would be easy (three rows of white, two empty rows, and three rows of black) but could that perhaps be improved? $\endgroup$ – supercat Oct 15 '14 at 22:08
  • $\begingroup$ 48 sounds like the max, since my only other solution (diagonal empty) only gets 42. Maybe it would be a good question to ask. $\endgroup$ – JonTheMon Oct 15 '14 at 23:12
  • $\begingroup$ I don't know that it would be a good question unless there's something about it that people would find interesting. It would seem there are quite a few ways to get 48, though I don't know that enumerating all of them would be interesting. Perhaps a question of how to prove that 48 is maximal (if it is?) $\endgroup$ – supercat Oct 16 '14 at 0:38

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