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

332 • CHAPTER 12 Problem Solving

a research program that described problem solving as a process that involves search.

That is, instead of just considering the initial structure of a problem and then the new

structure achieved when the problem is solved, Newell and Simon described problem

solving as a search that occurs between the posing of the problem and its solution.

The idea of problem solving as a search is part of our language. People commonly

talk about problems in terms of “searching for a way to reach a goal,” “getting around

roadblocks,” “hitting a dead end,” and “approaching a problem from a different angle”

(Lakoff & Turner, 1989). We will introduce Newell and Simon’s approach by describing

the Tower of Hanoi problem.

NEWELL AND SIMON’S APPROACH

Newell and Simon (1972) saw problems in terms of an initial state—conditions at the

beginning of the problem—and a goal state—the solution of the problem. ● Figure 12.10a

shows the initial state of the Tower of Hanoi problem as three discs stacked on the left

peg, and the goal state as these discs stacked on the right peg. Try solving this problem

by following the instructions in the demonstration.

In addition to specifying initial and goal states of a problem, Newell and Simon also introduced the

idea of operators—actions that take the problem from one state to another. For the Tower of Hanoi

problem, the following rules specify which actions are allowed and which are not (see Figure 12.10b):

1. Discs are moved one at a time from one peg to another.


2. A disc can be moved only when there are no discs on top of it.


3. A larger disc can never be placed on top of a smaller disc.

As you try solving this problem, count the number of moves it takes to get from the initial

to the goal state.

Initial state Goal state

123 123

(a)

(b)

Rule 1: Move

one disc at a time

from one peg to

another.

Rule 2: Can

move disc only

when no discs

are on it.

Rule 3: Larger

disc cannot be put

on smaller disc.

●FIGURE 12.10 (a) Initial and goal states for the Tower of Hanoi problem. (b) The

rules for actions allowed when solving the problem. (Source: Based on K. Kotovsky, J. R. Hayes, &

H. A. Simon, H. A., “Why Are Some Problems Hard? Evidence From Tower of Hanoi,” Cognitive Psychology, 17,

248–294, 1985.)

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