MATHS WEEK is under way and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go! You can check out other events being held over the next week here. 

Yesterday, we encountered the ancient Greek Demochares and a puzzle about his age which shows us that mathematical puzzles are long a part of human culture.

The great English Puzzler Henry Dudeney (who lived from 1857 to 1930) was one of the greatest creators and collectors of such teasers. He published a lot of questions related to age – here is one of them.

1. Can you find Robinson’s age?

Robinson said:

My brother is two years older than I,
my sister is four years older than he,
my mother was 20 when I was born,
and I was told yesterday that the average age of the four of us is 39 years.

What was Robinson’s age?

And here are two more age-related puzzles.

2. Anne’s age is three times her son’s age. In ten years’ time it will be twice her son’s age.
How old is Anne now?

3. Don was three times as old as Bill ten years ago. In ten years’ time Don will be only twice as old as Bill. How old are they now? 

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Sunday’s puzzle: The answers

1. 60

Demochares lived 15 years as a boy, 12 as a young man, 20 as a man, and 13 years as an old man; in all 60.

He lived 1/4 + 1/5 + 1/3 + 13 years

1/4 + 1/5 + 1/3 = (15 + 12 +20)/60 = 47/60.

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That leaves 13/60 for the remainder of his life which was 13 years. Therefore his whole life was 60 years.

2. 12: Dan got 4, Éilis got 3 and Fiachra got 5

One third and one quarter were taken. One third and one quarter added together is seven
twelfths. We can’t add these fractions directly; we must convert them so they have the same denominator.

One third is 4/12 and one quarter is 3/12. We can add them now to 7/12. This leaves 5/12 which is how much Fiachra gets – ie, 5 sweets. If 5 sweets is 5/12 of the total, then the total must be 12.

3. 32: Aine got 16, Brian got 8 and Ciara got 8

If there were a half and a quarter gone then there was a quarter left. So, Ciara’s 8 sweets
were a quarter of the total. 

Come back tomorrow at 7.30pm for the answers to today’s questions and a brand new challenge.  

These puzzles were prepared exclusively for The Journal by Eoin Gill, co-founder and co-ordinator of Maths Week Ireland.