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Number of the Day — 4,900

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Edited by Richard Walker, Sunday 25 January 2026 at 20:51

Its claim to fame

equation sequence part 1 sum with variable number of summands one squared plus two squared plus three squared plus ellipsis plus 24 squared equals part 2 70 squared equals part 3 4900

and (unless you count one squared equals one squared ) this is the only square number that is a sum of squares of consecutive numbers starting at 1. This means that if you make a square pyramid by piling up cannonballs the only possible number of cannonballs is 4,900.

Proving 4900 is the only solution is not at all easy. The first attempts were in the late 19th century and different proofs were published over a span of more that 100 years. See https://en.wikipedia.org/wiki/Cannonball_problem

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