Combinatorial Explorations in Su-Doku

Details Combinatorial Explorations in Su-Doku Combinatorial Explorations in Su-Doku

2008-03-29

arxiv.org/abs/0803.4253v1

Computer Science

Artificial Intelligence

Scientific paper

Su-Doku, a popular combinatorial puzzle, provides an excellent testbench for heuristic explorations. Several interesting questions arise from its deceptively simple set of rules. How many distinct Su-Doku grids are there? How to find a solution to a Su-Doku puzzle? Is there a unique solution to a given Su-Doku puzzle? What is a good estimation of a puzzle's difficulty? What is the minimum puzzle size (the number of "givens")? This paper explores how these questions are related to the well-known alldifferent constraint which emerges in a wide variety of Constraint Satisfaction Problems (CSP) and compares various algorithmic approaches based on different formulations of Su-Doku.

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