330 • CHAPTER 12 Problem Solving
When he compared the performance of the two groups, he found that the group that
had been presented with the boxes as containers found the problem more diffi cult
than did the group that was presented with empty boxes. Robert Adamson (1952)
repeated Duncker’s experiment and obtained the same result: Participants who were
presented with empty boxes were twice as likely to solve the problem as participants
who were presented with boxes that were used as containers (● Figure 12.6).
The fact that seeing the boxes as containers inhibited using them as supports is
an example of functional fi xedness. Another demonstration of functional fi xedness is
provided by Maier’s (1931) two-string problem, in which the participants’ task was
to tie together two strings that were hanging from the ceiling. This is diffi cult because
the strings are separated, so it is impossible to reach one of them while holding the
other (● Figure 12.7). Other objects available for solving this problem were a chair
and a pair of pliers.
To solve this problem, participants needed to tie the pliers to one of the strings to
create a pendulum, which could then be swung to within the person’s reach. Two things
are particularly signifi cant about this problem. First, 60 percent of the participants did
not solve the problem because they focused on the usual function of pliers and did
not think of using them as a weight. Second, when Maier set the string into motion by
“accidentally” brushing against it, 23 of 37 participants who hadn’t solved the prob-
lem after 10 minutes proceeded to solve it within 60 seconds. Seeing the string swing-
ing from side to side apparently triggered the insight that the pliers could be used as
a weight to create a pendulum. In Gestalt terms, the solution to the problem occurred
once the participants restructured their representation of
how to achieve the solution (get the strings to swing from
side to side) and their representation of the function of the
pliers (they can be used as a weight to create a pendulum).
Both the candle problem and the two-string problem
were diffi cult because of people’s preconceptions about the
uses of objects. These preconceptions are a type of mental
set, a preconceived notion about how to approach a prob-
lem, which is determined by a person’s experience or what
has worked in the past. In these experiments mental set was
created by people’s knowledge about the usual use of objects.
The Gestalt psychologists also showed how mental set
can arise out of the situation created as a person solves a
problem. An example is provided by the Luchins water-jug
problem, in which participants are given three jugs of differ-
ent capacities and are required to use these jugs to measure
out a specifi c quantity of water, as shown in ● Figure 12.8
(Luchins, 1942). Problem 1 is solved by fi rst fi lling the
127-cup jug (B) and then pouring the water from B into
A once and into C two times, thereby subtracting 27 cups
and leaving 100 in jug B. This solution, which can be
stated by the formulaDesired quantity = B − A − 2Cworks for all of the problems in Figure 12.8. However,
problems 7 and 8 can be solved more simply by using only
jugs A and C. For problem 7: Pour A (15) and C (3) into
a container to arrive at 18 (Desired quantity = A + C). For
problem 8: Fill jug A (28) and then pour from A into C (3),
to leave 25 in A (Desired quantity = A – C).
A. S. Luchins (1942) had some participants begin with
problem 1 and do each problem in sequence through problem 8 (the mental set group),
and had other participants solve only problems 7 and 8 (the no mental set group).
● Figure 12.9 compares the performance of the two groups. All of the participants
in the no mental set group used the shorter solution for problems 7 and 8, whereasBoxes
emptyBoxes as
containers100Percent solving problem050●FIGURE 12.6 Results of
Adamson’s (1952) replication of
Duncker’s candle problem. (Source:
Based on R. E. Adamson, “Functional
Fixedness as Related to Problem Solving,”
Journal of Experimental Psychology, 44,
288–291, 1952.)●FIGURE 12.7 Maier’s (1931) two-string problem. As hard as
Sebastian tries, he can’t grab the second string. How can he tie
the two strings together? (Source: Based on N. R. F. Maier, “Reasoning in
Humans: II. The Solution of a Problem and Its Appearance in Consciousness,”
Journal of Comparative Psychology, 12, 181–194, 1931.)Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.