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# Maths Week: Your Sunday puzzle

## Fancy another 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!

Maths and Rabbit Reproduction and Covid

Imagine you have to calculate your taxes.

Imagine it’s 15% of your earnings. You know what to do- multiply your income by 15 and divide by 100.

Imagine you’re in Rome or Medieval Europe.

You earn MDC units and you have to pay XV on every C.

Simply multiply MDC by XV and divide by C.

Not very simple?

Don’t worry, just pop down to the corner and you’ll find a mathematician that will calculate it for you.

The Islamic world was using nine numerals plus zero in the manner we use today. After travelling and learning around the Mediterranean world, the 32 Year-old Leonardo of Pisa published his Liber Abaci (Book of Calculations) in 1202, which introduced the Hindu-Arab numerals and algebra to Europe.

This was a revolution, allowing speedier calculations for book-keeping, interest calculations, reckoning of weights and measures and all areas of commerce and administration.

Liber Abaci was one of the rare books that influenced the course of history. Leonardo died in 1250 and is known today by his nickname Fibonacci.

In Liber Abaci, he also posed the following famous problem.

Suppose you have a male and female rabbit living in a field.

How many rabbits will there be after 1 year?

The answer of course is “we can’t know”. Probably none if a fox gets them.

However, we can make an estimate making certain assumptions using maths that can give us a good guide to what could happen in the real world.

Leonardo tells us to make the following assumptions:

• The two rabbits are babies at the start
• No rabbits are eaten by predators. (They all live and stay in the field).
• Each female reproduces every month. A baby rabbit is ready to mate after one month.
• Each time a rabbit reproduces she gives birth to two baby rabbits (one male and one female)

Can you figure out how many rabbits we will have under these conditions?

Hint: It might be a good strategy to work through a few generations of rabbits and look for a pattern.

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 the answer to today’s puzzle

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Four suffer from all three ailments

The Method:

You could draw out a table but it will be easier if you represent it visually with a Venn diagram.

Enter all the information on the Venn diagram.
We know there are 3 patients that have either gangrene alone or dysentery alone.
All this adds up to 24.
There are 30 patients in total, so 4 must make up the “all three” category.

Source: Eoin Gill