A Dynamic Programming Solution to the n-Queens Problem

Rivin, I. and R. Zabih, A dynamic programming solution to the n-queens problem, Information Processing Letters 41 (1992) 253-256. The n-queens problem is to determine in how many ways n queens may be placed on an n-by-n chessboard so that no two queens attack each other under the rules of chess. We describe a simple O( f(n)8”) solution to this problem that is based on dynamic programming, where f(n) is a low-order polynomial. This appears to be the first nontrivial upper bound for the problem.