LITS

LITS is a binary determination logic puzzle published by the Japanese puzzle company Nikoli, typically presented on a ten by ten grid. The grid is divided into regions called polyominoes, each containing at least four cells, and the solver must shade exactly one tetromino, a four-cell shape, inside every region. Two rules constrain the shading: no two shaded tetrominoes of the identical shape, counting rotations and reflections, may sit directly next to each other across a region boundary, and every shaded cell in the whole grid must connect into one single contiguous shape that also avoids forming any two by two block of shaded cells, the same no-pool rule used in the puzzle Nurikabe. The puzzle first appeared in Puzzle Communication Nikoli issue 106 under the name Nuruomino, combining the Japanese word for painting with the word for polyomino. By issue 112 the name had changed to LITS, an acronym for the four tetromino shapes a finished grid may use: the L shape, the straight I shape, the T shape, and the skew S shape. Deciding whether a given LITS grid has any valid solution at all is an NP complete problem in computational terms.