Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game effectively using constraint programming is hard. This abstract presents the game, contributes new generalized variants of the game suitable for benchmarking and testing, and describes a model for the presented variants.

The question of the top possible score in the standard game is an open challenge.

The regular constraint is a powerful global constraint with many possible uses. It was introduced to model certain common constraints in rostering problems. In this paper we show how to use it to model placement problems with irregular shapes. The technique is illustrated by solving Pentominoes and Solitaire Battleships. The efficiency of the basic model is improved by projecting out irrelevant information. Experimental results on Pentomino packing benchmark instances indicate that this simple approach can be competitive with specialized algorithms. From the applications we can identify some areas for improvement in the implementation of regular constraints.