Abstract
1. THE PROBLEM. One of the most familiar brand names in the world of toys is LegoTM; the name immediately brings interlocking building blocks to mind. Interlocking blocks fit together in restricted ways. Typically, a block of order q (length q + 1) has q + 1 protrusions on its top and q + 1 indentations on its bottom, so that the indentations on the bottom of one block can lock on to the protrusions on the top of another. Here q is a positive integer, and the width and height of a block are unimportant. For q = 1 and q = 2, Figure 1 shows the q ways in which one block can sit on top of two others.
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