Why are some problems hard? Evidence from Tower of Hanoi

This paper analyzes the causes for large differences in difficulty of various isomorphic versions of the Tower of Hanoi problem to seek and find causes for the differences in features of the problem representation.

Abstract

This paper analyzes the causes for large differences in difficulty of various isomorphic versions of the Tower of Hanoi problem. Some forms of the problem take 16 times as long to solve, on average, as other versions. Since isomorphism rules out size of task domain as a determinant of relative difficulty, these experiments seek and find causes for the differences in features of the problem representation. Analysis of verbal protocols and the temporal patterning of moves allows the problem-solving behavior to be divided into exploratory and final-path phases. Entry into the final-path phase depends on acquisition of the ability to plan pairs of moves, an achievement made difficult by the working memory load it entails. This memory load can be reduced by automating the rules governing moves, either through problem exploration or training. Once automation has occurred, the solution is obtained very rapidly. Memory load is also proposed as the locus of other differences in difficulty found between various problem representations.