What Makes Some Problems Really Hard: Explorations in the Problem Space of Difficulty

摘要

The paper identifies two sources, one larger, one smaller, of the great difficulty encountered by subjects solving the Chinese Ring Puzzle. With a two-hour time allotment, almost none of our college student subjects were able to solve the puzzle unless they were given a demonstration of how to move in the problem space, and even with that help only half of the subjects obtained solutions. The authors show that the processing demands imposed by the need to discover how to make moves, rather than other features of the problem search space, are the source of the inordinate difficulty of this problem. Evidence for this view comes from a set of isomorphs that were designed in a manner that digitized the moves, which in the original version have analog qualities. These digital isomorphs, which incorporated varying amounts of information about moves, were solvable by almost all subjects, with average solution times of 10 to 25 minutes, depending on isomorph type. The digitized problems still required considerable effort for their solution. The difficulty of these problems in digital form, is particularly surprising given the shape of the problem search space. In our examination of the sources of difficulty for this problem, we also studied the transfer of skill between different isomorphs. The investigation of transfer of training showed that problem representational features such as move operator compatibility, move difficulty and the presence or absence of move legality cues determined the amount of transfer. (kr)