Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Enigma 1225: Prolog-assisted solution of a puzzle using discrete mathematics
Computers & Mathematics with Applications
Generating effective symmetry-breaking predicates for search problems
Discrete Applied Mathematics
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
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This paper presents a constraint programming approach to the Enigma 1225, a mathematical puzzle published in the New Scientist magazine in February 2003. An approach based on Prolog was published recently. In this paper we give a constraint programming perspective on the problem, highlighting the differences between the two methodologies. We show how problem-specific knowledge can be easily incorporated into a constraint-based approach, giving an efficient constraint model for the generalized version of the puzzle. From the constraint programming point of view, the Enigma 1225 puzzle exhibits interesting symmetries, that can be eliminated using only a small number of constraints added to the model. Furthermore, properties of the puzzle can be used to derive a strong constraint propagation scheme that limits the search once an optimal solution has been found.