The Eight Queens Problem

SAT solvers and symmetries

The latest two posts have been about the eight queens problem: how to place eight queens on a chessboard so that no two queens attack each other.

One way to solve the problem is to have 64 Boolean variables, one for each square on the board, representing whether the square contains a queen. But how do you expression the eight queens problem in terms of logical expressions of these variables? I show how here.

(If you’re interested in Boolean SAT problems, see the links at the bottom of the post to posts by Wayne Joubert on SAT solvers.)

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There are 12 families of solutions to the eight queens problem. One is especially ordered and one is especially disordered. The post on special solutions explains in what sense the solutions are special.

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Thanks for following. Enjoy reading!