Solving combinatorial problems: The 15-puzzle

• Published in: Memory & cognition Vol. 33; no. 6; pp. 1069 - 1084
• Main Authors: Pizlo, Zygmunt, Li, Zheng
• Format: Journal Article
• Language: English
• Published: Austin, TX Psychonomic Society 01.09.2005; Springer Nature B.V
• Subjects: Algorithms; Approximation; Biological and medical sciences; Cognition. Intelligence; Experiments; Fundamental and applied biological sciences. Psychology; Human performance; Human subjects; Humans; Judgment; Problem Solving; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Puzzles; Reasoning. Problem solving; Traveling salesman problem; Human; Problem solving; Cognition; Experimental study; Combinatorial problem
• ISSN: 0090-502X; 1532-5946; 1532-5946
• DOI: 10.3758/BF03193214

We present a series of experiments in which human subjects were tested with a well-known combinatorial problem called the 15-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.