I’ve just read a classic psychological study* by Mary Gick and Susan McGarry, published in 1992. They conducted a series of four experiments to test whether your problem solving ability could be enhanced, if you had previously worked on a very similar type of problem. The target problem was the “mutilated checkerboard” problem (see figure at right). The problem is: “You are given a checkerboard and 32 dominoes. Each domino covers exactly two adjacent squares on the board. Thus, the 32 dominoes can cover all 64 squares of the checkerboard. Now suppose two squares are cut off at diagonally opposite corners of the board. If possible, show how you would place 31 dominoes on the board so that all of the 62 remaining squares are covered. If you think it is impossible, give a proof of why.”
In order to solve the problem, you have to discover the “parity” rule: No covering is possible, because each domino must cover one black and one red square, and because the two black corners have been removed, there are two more red squares than black squares.
Gick and McGarry then developed several other problems, that are analogous to the mutilated checkerboard in that they require a “parity representation” to be solved. Some of them were easy to solve, and some were harder. For example, the easy problem was: 20 men and 20 women are at a dance. If two of the women leave, is it then possible for the remaining people to form 19 male-female couples? Solving this problem did not later increase performance on the checkerboard problem (which I find a bit surprising, but continue reading…)
Then, they developed another analogous problem, with men and women being seated at a dinner party. Most people failed to solve this problem at first, but when they received a hint, they could solve it. And the surprise is: failing at first, but then getting the hint, resulted in increased performance on the checkerboard problem! Their conclusion:
“source solution failures that are analogous to target solution failures facilitate spontaneous transfer” (p. 635). Wonderful paper!
*Journal of Experimental Psychology: Learning, Memory, and Cognition 1992, Vol. 18, No. 3,623-639