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Creative Insight: The Redistribution Theory 121

Figure 4.6. Two examples of Match Stick Arithmetic Problems.

This idea was put to the test by Guenter Knoblich and myself in a series
of experiments with so-called Match Stick Arithmetic Problems, puzzles that
exhibit a strong mismatch between prior experience and the requirements of
the problem. In such a problem, the goal is to correct an incorrect arithmetic
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equation, written in Roman numerals made out of match sticks, by moving
exactly one match stick to another place in the equation. Figure 4.6 shows two
examples of this type of problem. The solutions to all Match Stick Arithmetic
Problems used in our studies consist of exactly one step. There is little doubt
that an average educated adult in Western culture will spontaneously activate
his arithmetic knowledge when confronted with such a problem. But to solve
it, he has to override the constraints normally followed in arithmetic. The solu-
tion requires actions that are not valid in arithmetic.
Consider the differences between problems 1 and 2 in Figure 4.6. Each
problem requires a single step and so has the same objective difficulty.
Nevertheless, we found in a series of experiments that the second problem
is more difficult than the first. The general principle of mismatches to prior
knowledge does not suffice to explain this difference, because both problems
will activate unhelpful arithmetic knowledge.
Guenther Knoblich and I hypothesized that the differentiating factor is the
scope of the representational shift that has to take place. To solve the top prob-
lem, the person only has to override the constraint on altering the numbers in an
equation, while leaving the structure of the equation intact. To solve the bottom
problem, the structure and meaning of the entire equation have to be revised.
Precise analysis of exactly which constraints have to be relaxed to solve a given