In this paper, a rectilinear jigsaw puzzle is taken up as a specialized placement problem such that it has at least one solution of placement, but not so many in general. In order to solve this problem, instead of adopting the well known iterative method, a new game-theoretic algorithm is developed by translating the problem to a checkmate problem of a game analogous to chess or shogi. It is proved by numerical experiments that this works well with good efficiency.
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