Diophantus' Riddle

How Old Was Diophantus?

An Ancient Riddle


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This is surely the ultimate mathematical riddle and most probably the first. It is about the life of Diophantus, the father of algebra, who lived in the second century. It comes from a fifth century Greek anthology of number games and puzzles created by Metrodorus. One of the problems (sometimes called his epitaph) is the riddle you see above.

The riddle can be written as an equation where \(x\) is the age Diophantus died.

$$\frac x6 + \frac x{12} + \frac x7 + 5 + \frac x2 + 4 = x$$

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