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. 

Puzzle two: Demochares

Puzzles are an effective way to develop mathematical thinking and problem-solving skills. It is amazing how long human beings have engaged with mathematical puzzles. Many puzzles in circulation today are merely variations of Greek, Indian, Arabic or European medieval puzzles.

Demochares was an Athenian orator and statesman from the 3rd or 4th century BC. It is believed that he died in 275 BC but it is not certain when he was born. However, a puzzle has come been handed down to us that gives us a clue*.

1. How long did Demochares live for?

Demochares lived for a quarter of his whole life as a boy,
for a fifth part of it as a young man,
and for a third as a man,
and when he reached grey old age, he lived thirteen years more.
How long did Demochares live for?

If you don’t like that one, try a more modern slant with these two.

2. At Hallowe’en the children divided up sweets. Dan took one third, Éilis took one quarter and that left 5 for Fiachra. How many sweets were there altogether?

3. Another group also divided up sweets. Aine took half, Brian took a quarter and Ciara was left with 8 sweets. How many sweets were there altogether?

*Translation by Paton, W. R. 1857-1921

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Saturday’s puzzle: The answer  

1. 495

2. 6853

3. 1, 2, 3

4. 1.5, 3.

5. Nora 10, Will 14

6. 1 butter; 4 flour; 2 eggs

7. 1,000 words

8. 6 minutes

9. 3

10. Anne: 48; Brian: 21

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.