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356 Decision framing and cognitive inertia
Initial state
Intermediate
states
Goal state
Jug 1 Jug 2 Jug 3
8−8
8−3
8−3
8−6
8−6
5−0
5−5
5−2
5−2
5−0
3−0
3−0
3−3
3−0
Figure 14.1 – Moves to attain the goal state in the first water-jug problem
What are the moves to change the initial state of the jugs and the
goal state? Figure 14.1 gives the easiest series of moves. It is worthwhile
working through this figure.
First, jug 1 is used to fill jug 2. Then, jug 2 is used to fill jug 3. Next, the
contents of jug 3 are poured into jug 1 and then, finally, the contents of
jug 2 are poured into jug 3.
Next, consider an 8-pint jug filled with water, an empty 5-pint jug and
a 3-pint jug containing 1 pint of water (i.e. 8–8, 5–0, 3–1). Figure 14.2
gives a series of moves to reach the goal state (8–6, 5–0, 3–3). Let us
again follow the logic of the moves.
First, jug 1 is used to fill jug 2. Then, jug 2 is used to fill jug 3. Next,
jug 3 is poured into jug 1 and then, finally, the contents of jug 2 poured
into jug 3. Do you follow the logic? In fact, should you follow the logic?
If you feel that you should, then think again! A more efficient solution
to the problem would be, simply, to pour the contents of jug 1 into
jug 3. Luchins and Luchins 1 used problems similar to this with two
groups of people. One group were given a series of problems that could
only be solved by very similar sequences of moves. When this group
were given a problem that could be solved by the familiar sequence
or by a much simpler sequence then the group applied the familiar,
previously successful, sequence. In fact they did not ‘see’ the simpler
Initial state
Intermediate
states
Goal state
3−2
Jug 1 Jug 2 Jug 3
8−8
8−3
8−3
8−6
8−6
5−0
5−5
5−3
5−3
5−0
3−1
3−1
3−3
3−0
Figure 14.2 – Moves to attain the goal state in the second water-jug problem
3−3