Cognitive Psychology: Connecting Mind, Research and Everyday Experience, 3rd Edition

We will now consider the mutilated checkerboard problem, which provides another

example of how the way a problem is stated can infl uence its diffi culty.

A checkerboard consists of 64 squares. These 64 squares can be completely covered by placing

32 dominos on the board so that each domino covers two squares. If we eliminate two corners

of the checkerboard, as shown in ● Figure 12.15, can we now cover the remaining squares with

31 dominos?

See whether you can solve this problem. A solution would be either a “yes” or “no” answer

plus a statement of the rationale behind your answer.

Craig Kaplan and Herbert Simon (1990) used this problem and variations of it to

study how the way a problem is stated affects its diffi culty. There were four conditions

in their experiment. Each group received a different version of the problem. The four

conditions, shown in ● Figure 12.16, were (1) blank—a board with all blank squares;

(2) color—alternating black and pink squares as might appear on a regular checker-

board; (3) black and pink—the words black and pink on the board; and (4) bread and

butter—the words bread and butter on the board.

The key to solving the problem is to realize that when a domino is placed on

the board so it covers just two squares, it is always covering two squares that are

different (pink and black, for example). There is no way to place a domino so it cov-

ers two pink squares or two black squares. Therefore, for 31 dominos to cover the

board there must be 31 pink squares and 31 black squares. However, this isn’t the

case, because two pink squares were removed. Thus, the board can’t be covered by

31 dominos.

All four versions of the checkerboard problem have the same board layout and the

same solution. What is different is the information on the squares (or lack of informa-

tion on the blank board) that can be used to provide participants with the insight that a

domino covers two squares and that these squares must be different colors. Not surpris-

ingly, participants who were presented boards that emphasized the difference between

●FIGURE 12.15 Mutilated checkerboard problem. See demonstration for instructions.

Modern Research on Problem Solving • 337

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