Geometric particle swarm optimization (GPSO) is a recently introduced generalization of traditional particle swarm optimization (PSO) that applies to all combinatorial spaces. The aim of this paper is to demonstrate the applicability of GPSO to non-trivial combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as a nontrivial constrained combinatorial problem. We apply GPSO to solve the sudoku puzzle. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity General Terms Theory Keywords Particle Swarm Optimisation, Metric Space, Geometric Crossover, Sudoku