# Bachet de Méziriac, Claude-Gaspar (1581–1638)

Claude Bachet was a poet and early mathematician of the French Academy, best
known for his translation in 1621 of Diophantus's *Arithmetica*, the book that Pierre de Fermat was reading when he inscribed the margin with his famous Last
Theorem.

Bachet is also remembered as a collector of mathematical puzzles, many of
which, including river-crossing
problems, measuring
and weighing puzzles, number tricks, and magic
squares, he published in *Problèmes plaisans et délectables qui font
par les nombres* (1612). One of the puzzles is to find the least number
of weights that can be used on a scale pan to weigh any integral number
of pounds from 1 to 40 inclusive, if the weights can be placed in either
of the scale pans. The answer is four: 1, 3, 9, and 27 pounds.

On a slightly more serious note, Bachet observed that apparently every positive
number can be expressed as a sum of at most four squares; for example, 5
= 2^{2} + 1^{2} , 6 = 2^{2} + 1^{2} + 1^{2},
7 = 2^{2} + 1^{2} + 1^{2} + 1^{2}, 8 = 2^{2} + 2^{2}, and 9 = 3^{2}. The case of 7 shows that sometimes
three squares wouldn't be enough. Bachet said he had checked this for more
than 300 numbers but didn't know how to prove it. It wasn't until the late
18th century that Joseph Lagrange supplied
a complete proof.

## Reference

1. Underwood, Dudley. "The First Recreational Mathematics Book." *Journal
of Recreational Mathematics*, 3, 164-169, 1970.