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?

The solution to this and other Transum puzzles, exercises and activities are available when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here.

A Transum subscription also gives you access to the 'Class Admin' student management system and opens up ad-free access to the Transum website for you and your pupils.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items I have chosen and recommend to get you started. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

## 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.