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The Four Corners Puzzle is a good example of an interlocking structure with an intriguing geometry and attractive shape but which is trivially simple as an assembly puzzle. To make it also challenging, the concept of color symmetry is introduced. Imagine the end blocks colored four different colors as indicated in Fig. 103.
Fig. 103
Problem: assemble the above pieces in color symmetry. Advanced problem: discover all the possible ways of assembling these pieces in color symmetry. In order to solve this problem, we must first define exactly what is meant here by color symmetry. When a multicolored polyhedral puzzle is said to be assembled in color symmetry, it meets the following test: choose any color and change it to black. Change all the other colors to white. No matter which color was changed to black, the result is the same, and the black pattern has an axis of symmetry.
The four different ways in which the Four Corners Puzzle can be assembled in color symmetry are represented in Fig. 104 in black and white. The one on the left, in which each "corner" is a solid color, is the easiest and most obvious and is how the puzzle got its name. Each has a pair of solutions.
Fig. 104
Finally, to extract one more bit of recreation from this puzzle, discover the 24 ways of assembling it such that the patterns of all four colors are identical but not symmetrical. You may skip the 3,808 ways that do not have either property. Hint: in general, these color symmetry problems are not the type that one solves by trial and error. One must try to discover the principles involved and the simple rules that transform one solution into another. You may not even need the physical pieces.
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