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First, let's try stating the cannonball problem:
Cannonballs are stacked in a square pyramid, with one on top, four on the level below, nine on the level below that, and so on, with n2 on the bottom level. If the total number of cannonballs is a square, how many levels are there?
After the trivial answers of zero and one, the next answer is 24, since 12 + 22 + ... + 242 = 4900 = 702. It turns out that these are the only possible answers, but the proof is difficult.
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