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dingus  ·  2545 days ago  ·  link  ·    ·  parent  ·  post: A puzzle: How to most quickly destroy the tank?

What I'm trying to say is that all black squares have to be bombed before their adjacent white squares, so bombing all blacks and then all whites is the same as bombing them in some other pattern that meets the same requirements and outputs the same number(for instance, bombing all whites in a row then bombing all blacks in a row). The checkerboard is the smallest that meets the requirements because it pairs every black with one adjacent white (plus the extra one), so if you added one more black it would require that two pairs of blacks exist.

EDIT:

in fact, I suppose you could use that pairing scheme to always bomb any configuration of squares in at most nSquares*3/2 + remainders