336 • CHAPTER 12 Problem Solving
The Acrobat Problem
Three circus acrobats developed an amazing routine in which they jumped to and from
each other’s shoulders to form human towers (● Figure 12.14). The routine was quite
spectacular because it was performed atop three very tall fl agpoles. It was made even more
impressive because the acrobats were very different in size: The large acrobat weighed
400 pounds; the medium acrobat, 200 pounds; and the small acrobat, a mere 40 pounds.
These differences forced them to follow these safety rules:- Only one acrobat may jump at a time.
- Whenever two acrobats are on the same fl agpole, one must be standing on the
shoulders of the other. - An acrobat may not jump when someone is standing on his or her shoulders.
- A bigger acrobat may not stand on the shoulders of a smaller acrobat.
At the beginning of their act, the medium acrobat was on the left, the large acrobat
in the middle, and the small acrobat on the right (initial state; Figure 12.14a). At the end
of the act, they were arranged small, medium, and large from left to right (goal state;
Figure 12.14b). How did they manage to do this while obeying the safety rules?
The acrobat problem can be solved by making just 5 moves, as indicated by the
solution shown in ● Figure 12.29a (page 357). K. Kotovsky and coworkers (1985) found
that it took their participants an average of 5.63 minutes to solve this problem. However,
when they made one small change in the problem, it became much more diffi cult.The Reverse Acrobat Problem
The reverse acrobat problem is the same as the acrobat problem, except that rule 4 above
was changed to state that a smaller acrobat cannot stand on a larger one.Although this version of the problem can be solved in the same number of steps as
the original acrobat problem (see Figure 12.29b), Kotovsky’s participants took an aver-
age of 9.51 minutes to solve the reverse acrobat problem. There are a number of pos-
sible reasons that the reverse acrobat problem is more diffi cult. One possibility is that
the idea of a 400-pound acrobat standing on the shoulders of a 40-pound acrobat is not
consistent with our knowledge of the real world, in which it would be highly unlikely
that the small acrobat could support the large one. In addition, it may be harder to
visualize larger acrobats on top of smaller ones, which would make the problem more
diffi cult by increasing the load on the problem-solver’s memory. Whatever the reason,
these results show that to understand problem solving, we need to go beyond analyzing
the structure of the problem space.Initial state Goal state(a) (b)●FIGURE 12.14 (a) Initial and (b) goal states of the acrobat problem.Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.