Diophantus Puzzle

Diophantus was a Greek mathematician. Little is known about the life of Diophantus except for an algebraic riddle from around the early sixth century. The riddle states:

Here lies Diophantus,’ the wonder behold.
Through art algebraic, the stone tells how old:
‘God gave him his boyhood one-sixth of his life,
One twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage
After attaining half the measure of his father’s life chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.’

How many years did Diophantus live based on the riddle?


Based on the riddle, we can come up with the following equation:

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x

Where x is Diophantus’s age at the time of his death. Solving for x gives a value of 84.

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