Understanding Psychology (10th Ed)

 KINDS OF PROBLEMS 
Typically, a problem falls into one of the three categories shown in Figure 3: arrange-
ment, inducing structure, and transformation. Solving each type requires somewhat 
different kinds of psychological skills and knowledge (Spitz, 1987; Chronicle, Mac-
Gregor, & Ormerod, 2004). 
Arrangement problems require the problem solver to rearrange or recombine ele-
ments in a way that will satisfy a certain criterion. Usually, several different arrange-
ments can be made, but only one or a few of the arrangements will produce a 
solution. Anagram problems and jigsaw puzzles are examples of arrangement prob-
lems (Coventry et al., 2003). 
In problems of inducing structure, a person must identify the existing relation-
ships among the elements presented and then construct a new relationship among 
them. In such a problem, the problem solver must determine not only the rela-
tionships among the elements but also the structure and size of the 
elements involved. In the example shown in Figure 3, a person must 
fi rst determine that the solution requires the numbers to be consid-
ered in pairs (14-24-34-44-54-64). Only after identifying that part of 
the problem can a person determine the solution rule (the fi rst num-
ber of each pair increases by one, while the second number remains 
the same).
The Tower of Hanoi puzzle represents the third kind of problem—
transformation problems —that consist of an initial state, a goal state, and 
a method for changing the initial state into the goal state. In the Tower 
of Hanoi problem, the initial state is the original confi guration, the goal 
state is to have the three disks on the third peg, and the method is the 
rules for moving the disks (Mataix-Cols & Bartres-Faz, 2002; Emick & 
Welsh, 2005; Majeres, 2007). 
Whether the problem is one of arrangement, inducing structure, or 
transformation, the preparation stage of understanding and diagnosing 
is critical in problem solving because it allows us to develop our own 
cognitive representation of the problem and to place it within a per-
sonal framework. We may divide the problem into subparts or ignore 
some information as we try to simplify the task. Winnowing out nones-
sential information is often a critical step in the preparation stage of 
problem solving. 
“I don’t know about hair care, Rapunzel,
but I’m thinking a good cream rinse plus
protein conditioner might just solve
both our problems.”
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