A neat puzzle I just saw: You can place a black king anywhere you like on a chessboard of a given size m×n. Where do you place it such that you can place also the maximal number of white queens that do not attack the king? And how many of those queens can you place?
@Rosemary In a corner, I guess, because you rule out one row and one column no matter what, and as far as I can tell you can't do any better than ruling out only one diagonal... So that would leave mn - m - (n - 1) - (min(m, n) - 1) queens
@Trinket It seems to be a less interesting problem than I'd initially thought.
@Trinket @Rosemary Unless it's a trick question and it's like "well it doesn't say those are the *only* pieces you can place", in which case you get mn - 4 by putting the king in a corner surrounded by three other black pieces