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Problem of the Week 1178
Place queens on a 7 × 7 chessboard so that no three of them lie on a horizontal, vertical, or (45-degree) diagonal line, but so that the addition of a queen to any open square violates this condition. The idea is to do this with as few queens as possible.
For example, on a 3 × 3 board, the minimal solution uses four queens: Place them at four corners (or use a
There are many variations. I will discuss them in more detail in the solution post.
Thanks to Ed Pegg, Joseph DeVincentis, and Mark Rickert.
Source: Cooper, Pikhurko, Schmitt, Warrington, Martin Gardner's minimum No-3-in-a-line problem, Amer Math Monthly, 121, March 2014, 213-221.
© Copyright 2014 Stan Wagon. Reproduced with permission.
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