Theory Driven Hints in the Cheap Necklace Problem: A Preliminary Investigation

In this paper we conducted three experiments using the cheap necklace problem, which is regarded as an insight problem. The effects of two hints derived from two contemporary theoretical accounts of insight—Criterion for Satisfactory Progress theory (CSP) and Representational Change Theory (RCT)—were investigated. In Experiment 1, 78 participants made a single attempt at the problem, and significantly fewer participants given the CSP hint used an incorrect (maximizing) first move than participants given the RCT hint or control participants given no hint, Fisher’s exact test for 2x3 table, p = .029, with an approximation in χ² effect size, phi = .340. Experiment 2 explored the performance of 60 participants in the same hint conditions over ten problem-solving trials. The number of trials to solution was significantly fewer in the CSP hint condition than in the control condition, t(30) = 2.23, p = .033, η² = .14; this was not so for the RCT hint condition, t(30) = .44, p = .666, η² = .006. Furthermore, there were significantly fewer incorrect (maximizing) first moves in the CSP hint condition than in the other two conditions, F(2, 59) = 15.31, p < .001, η² = .35. The CSP hint here appears to promote the exploration of the problem space, such that the correct move may be found. The lack of effect of the RCT hint suggests in preliminary fashion that representational change may not be the primary cognitive process required to solve the cheap necklace problem. However, in Experiment 3 with 110 participants, the CSP and RCT hints were combined yielding a 75% solution rate over a 34.88% solution rate in the control condition, χ²(1) = 16.03, p < .001, phi = .402. This result indicates that perhaps aspects from both theories are employed during the problem solving process.