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Solving combinatorial problems: The 15-puzzle

Abstract

We present a series of experiments in which human subjects were tested with a well-known combinatorial problem called the15-puzzle and in different-sized variants of this puzzle. Subjects can solve these puzzles reliably by systematically building a solution path, without performing much search and without using distances among the states of the problem. The computational complexity of the underlying mental mechanisms is very low. We formulated a computational model of the underlying cognitive processes on the basis of our results. This model applied a pyramid algorithm to individual stages of each problem. The model’s performance proved to be quite similar to the subjects’ performance. Partial support for this research was provided by the Air Force Office of Scientific Research.

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Correspondence to Zygmunt Pizlo.

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Partial support for this research was provided by the Air Force Office of Scientific Research.

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Pizlo, Z., Li, Z. Solving combinatorial problems: The 15-puzzle. Memory & Cognition 33, 1069–1084 (2005). https://doi.org/10.3758/BF03193214

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Keywords

  • Reference State
  • Travel Salesman Problem
  • Goal State
  • Combinatorial Problem
  • Solution Path