Dosun-Fuwari is NP-complete

Abstract

Dosun-Fuwari is one of Nikoli's pencil puzzles, which is played on a rectangular grid of cells. Some of the cells are colored black, and the remaining cells are divided into rooms. The purpose of the puzzle is to place balloons and iron balls according to the following rules: Place one balloon and one iron ball in each room. Balloons (resp. iron balls) are light and float (heavy and sink), so they must be placed in the top (bottom) row of the grid of cells, or in a cell right under (over) a black cell or right under other balloons (over other iron balls). It is shown that deciding whether a Dosun-Fuwari puzzle has a solution is NP-complete.