Consider a triangular pyramid of balls, constructed by placing each ball (except those on the bottom) in the hollow formed by the three balls under it. If such a pyramid has 12 balls on the side of the bottom level, how many balls in total does it contain?

(In reply to by Eat Ham)

You are assuming a square bas for the pyramid, which does agree with the strict definition of a pyramid, but if you read the problem carefully, its says that the pyramid is "triangular" and that each ball rests in a hollow created by three (not four) balls in the next layer. Together, these clearly indicate that we are looking at not a square-based pyramid, but rather at a regular tetrahedron.

Posted by TomM on 2002-08-06 00:43:36