## Figure 144

The nine-dot problem (a) and its solution (b).

Another famous problem from the Gestalt school is Scheerer's (1963) nine-dot problem. As can be seen in Figure 14.4, the problem involves nine dots organised in a three-by-three matrix. In order to solve the problem one must draw four continuous straight lines, connecting all the dots without lifting the pencil from the paper. The correct solution is also shown in Figure 14.4 (although see Adams, 1979, for several wild but valid alternatives). Most people cannot solve the problem because, Scheerer maintained, they assume that the lines must stay within the square formed by the dots. In Gestalt terms, subjects had "fixated" on the shape of the dots and could not solve the problem for this reason. We shall see that later research has shown this is not the whole truth.

Problem-solving set: The water-jug problems

A final set of experiments produced by the Gestalt school that deserve mention are the water-jug experiments of Luchins and Luchins (1959, 1991; Luchins, 1942). These experiments are a special case of the general notion of fixation, where reproductive responses result in problem-solving failure rather than success. The Luchins termed the phenomenon problem-solving set. In a typical water-jug problem you have to imagine that you are given an eight-pint jug full of water, and a five-pint jug and three-pint jug that are empty (represented as 8-8, 5-0, 3-0, where the first figure indicates the size of the jug and the second the amount of water in that jug). Your task is to pour the water from one jug to another until you end up with four pints in the eight-pint jug and four pints in the five-pint jug (i.e., 8-4, 5-4, 3-0). Even though this problem appears straightforward it can take some time to solve (Table 14.1 shows one possible solution).

In order to demonstrate problem-solving set, Luchins and Luchins typically had two groups in their experiments: a set and a control condition. The set condition received a series of problems that could be solved using the same solution method, but the control group received problems that had to be solved using different methods. Then, both groups were given a test problem that could be solved using either a very simple method or the more complex method that the set condition subjects had been applying to all the previous problems. Unsurprisingly, the control group tended to use the simple method but the set group opted for the more complex method. In fact, they did not "see" the simpler method until it was pointed out to them. The set group had, in Gestalt terms, been fixated on the more complex method.

### Evaluating Gestalt theory and its legacy

The Gestalt psychologists attacked associationist views from two sides. First, they tried to show that problem solving was something more than the "mere" reproduction of learned responses; that it involved the productive processes of insight and restructuring. Recall Maier's demonstration of the

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