This is going to be the last of these notes. My goal was to cover the puzzles that I have found sufficiently interesting to be worthy of mention at Ada-Europe conferences. This year the conference was electronic and my Avatar and I gave a bit of a talk and ended by mentioning four puzzles.But first I must give the solution to the piles of cannonballs problem. Recall that soldiers were asked to pile their cannonballs into square pyramids such that the number of balls in each pyramid is itself a square number. Each layer of a square pyramid comprises a square number of balls. The first few pyramidal numbers are 1, 5, 14, 30, and 55. Note that 1 is of course a square number so the first pyramidal number that is also a square is simply 1. The question is what is the second pyramidal number that is also a square number?The answer is 4900 = 70~2.
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