An Extended Approach for the Automatic Solution of Tangram Puzzles Using Permutation Heuristics

Abstract

The Tangram is a geometric puzzle composed of seven polygonal pieces that can be combined to form different patterns. In combinatorial optimization, the task of solving Tangram puzzles is known to be NP-hard. In this paper, we present an extension of a recent computational method for the automatic solution of Tangram puzzles. The original work considers the largest-first heuristic, in which the pieces are positioned inside the puzzle region following a sequence from the largest to the smallest in area size. We present three additional permutation heuristics that generate different sequences to guide the pieces positioning inside the puzzle region. The effectiveness of the proposed heuristics is indicated by the application of the extended method on the solution of different Tangram puzzles. Combining the executed experiments, the extended method solved 93.33% of the patterns included in a dataset in an average time of 53.0s, while the original implementation solved 86.67% of the same dataset in an average time of 51.4s.