Polyomino Field puzzle generation method

A polyomino field is an arrangement of a set of polyominos such that they encircle an area.

A hard task is for a given set, find the maximal field.

How to generate a problem

Generate a circle of cells. Then split it up into polyominos (not necessarily all 4 squares). Given just those pieces, it is not easy to reconstruct a field with area more than that known max (or more).

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