OEIS A00170: The N-Queens Problem

We explore the classic N-Queens counting problem from the OEIS entry A00170. Learn why 0 solutions appear for N = 2 and N = 3, why there are 2 solutions for N = 4, 10 for N = 5, and 92 for the 8×8 board (the Project Euler connection). We’ll connect the combinatorics to graph theory via the N×N queen graph and maximum independent sets, discuss backtracking and constraint-satisfaction approaches, and dive into why there’s no simple closed form. We also cover asymptotic behavior: Simkin’s 2021 approximation ~0.143 n^n and related constants, and the staggering computational effort required for larger N. A rich case study in algorithm design, combinatorics, and number theory that shows just how deep a “simple” puzzle can be.

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