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Dublin: 7°C Wednesday 28 October 2020

Fancy a mathematics challenge? (And get the answer to yesterday’s puzzle.)

MATHS WEEK IS under way and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

“Man, what the f*\$k do the Greeks have to do with anything?”
-Rusty James in the film, Rumble Fish, 1983

When we think of maths, we don’t often think of its story and where it comes from.

The ancient Greeks are often considered to have discovered (or invented) maths.

However, while the Greeks developed their geometry and theorems over centuries, they in turn learned from others. In turn, they passed on their knowledge to others who built on it.

The name of Pythagoras (570–490 BCE) is known to secondary school pupils the world over, through his eponymous theorem. Even if that theorem might be remembered as “the square on the hippopotamus…”.

It states that for any right angle triangle, if you built a square on each side then the areas of the two smaller squares added together will equal the area of the larger square. It’s used a lot in architecture, construction and woodwork.

Of course, it may not have been Pythagoras who first discovered this relationship but he gets the credit, and it has been validated by many ingenious proofs.

Pythagorean triples are sets of three whole numbers where the two smaller numbers squared and added will equal the third number squared.

3, 4 and 5 are one such triple as are any set of multiples of them. In fact, lists of these triples are found on Mesopotamian cuneiform tablets that were compiled centuries before.

The followers of Pythagoras – the Pythagoreans – took a love of maths to extremes. They believed all things were made of numbers and that mathematics had a mystical meaning.

In Maths Week, we don’t go that far, but we think that maths can enrich all our lives and reveal mysteries of the universe. We can also use it to exercise our brains and help us develop problem-solving skills.

Here is one for you to try:

Three Pythagoreans are talking about their life journeys.

The eldest said to the second oldest, “Fifteen years ago I was your age.”

The second turned to the youngest and said, “Fifteen years ago I was your age.”

The youngest then replied: “The square of my age plus the square of your age is equal to the square of our venerable elder’s age.”

How old is each Pythagorean?

All puzzles are by Eoin Gill, the coordinator of Maths Week Ireland and director Calmast STEM Engagement Centre, Waterford Institute of Technology

Come back tomorrow for Wednesday’s puzzle and the answer for today’s.

120 gold coins

The method:

If we call the total number of coins X we can express all the amount in terms of X.

The three chief ministers got half the sum.

The priestesses each got the same as each minister. There were three ministers between them receiving half of the treasure. A half divided by 3 is a sixth, so they got one-sixth (i.e. 1/6 each) and that is what the priestesses got each.

So, the priestesses get:

The chancellor gets half of the priestess cut i.e.

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The food taster is left with 10 gold pieces.

So all these portions added together will equal the total amount, X

We can form an equation from this information like this:

We can’t add the fractions directly we must convert them to a common denomination. In the spirit of the Sumerians we can use 60: