Participant: Maybe it has to do with the words on the page? I haven’t tried any-
thing with that. Maybe that’s it. OK, dominos, umm, the dominos
can only fit... alright, the dominos can fit over two squares, and
no matter which way you put it because it cannot go diagonally, it
has to fit over a butter and a bread. And because you crossed out
two breads, it has to leave two butters left over so it doesn’t...
only 30, so it won’t fit. Is that the answer?Notice that the person was stuck at fi rst, and then suddenly got the answer after
realizing that the words bread and butter were important. By recording people’s thought
processes as they are solving the problem, the think-aloud protocol reveals a shift in
how the person perceived elements of the problem. This is very similar to the Gestalt
psychologists’ idea of restructuring. For example, remember the circle problem in Figure
12.2. The key to solving that problem was realizing that the line x was the same length
as the radius of the circle. Similarly, the key to solving the mutilated checkerboard prob-
lem is realizing that adjoining squares are paired, because a domino always covers two
different-colored squares in a normal checkerboard. Thus, in Gestalt terms, we could
say that the person creates a representation of the problem that makes it easier to solve.
Kaplan and Simon used two different colors to help their participants realize that
pairing of adjacent squares is important. But this has also been achieved in another
way—by telling the following story, which has parallels to the checkerboard problem.The Candle Problem
In a small Russian village, there were 32 bachelors and 32 unmarried women. Through
tireless efforts, the village matchmaker succeeded in arranging 32 highly satisfactory mar-
riages. The village was proud and happy. Then one drunken night, two bachelors, in a
test of strength, stuffed each other with pirogies and died. Can the matchmaker, through
some quick arrangements, come up with 31 heterosexual marriages among the 62 survi-
vors? (adapted from Hayes, 1978, p. 180)The answer to this problem is obvious. Losing two males makes it impossible to
arrange 31 heterosexual marriages. Of course, this is exactly the situation in the muti-
lated checkerboard problem, except instead of males and females being paired up, light
and dark squares are. People who read this story are usually able to solve the mutilated
checkerboard problem if they realize the connection between the couples in the story
and the alternating squares on the checkerboard. This process of noticing connections
between similar problems and applying the solution for one problem to other problems
is called the method of analogy. In the next section we will look more closely at how
analogy has been used in problem solving.- What is the psychological defi nition of a problem? Distinguish between well-
defi ned and ill-defi ned problems. - What is the basic principle behind the Gestalt approach to problem solving?
Describe how the following problems illustrate this principle, and also what
else these problems demonstrate about problem solving: the circle (radius)
problem; the candle problem; the two-string problem; the water-jug problem. - What is insight, and what is the evidence that insight does, in fact, occur as
people are solving a problem? - Describe Newell and Simon’s approach to problem solving, in which “search”
plays a central role. How does means-end analysis as applied to the Tower of
Hanoi problem illustrate this approach? - How do the acrobat problem and Kaplan and Simon’s mutilated checkerboard
experiment illustrate that the way a problem is stated can affect a person’s abil-
ity to solve the problem? What are the implications of this research for Newell
and Simon’s “problem space” approach?
TEST YOURSELF 12.1
Modern Research on Problem Solving • 339Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.