# How Old Was Diophantus?

## An Ancient Riddle

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.

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

Can you solve this equation to work out how old Diophantus was when he died?

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## More mathematical riddles:

If you liked this riddle you should try to solve some more such as these:

• How can it be that Percy will be 16 next year when he was only 13 the day before yesterday?
• If two's company and three's a crowd, what's four and five?
• When is eighteen hundred minus fifty the same as seventeen hundred plus ten?
• What is three sevenths of a chicken, two thirds of a cat and 50% of a goat?
• Who is most likely to be able to work out the square root of 121?

You will find these and many more mathematical riddles on the Maths Riddles page.

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