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# Maths Week: Your Sunday puzzle

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

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

Day two – Rabbits, Partridges, Pigeons and Sparrows

Sometimes in history, people are remembered for the wrong things.

The name Fibonacci will forever be associated with the sequence 1, 1, 2, 3, 5, 8, 13… (where every number is the sum of the two previous numbers). This sequence pops up in many places and surprisingly often in nature.

Leonardo of Pisa – better known as Fibonacci – presented this in a puzzle in his book Liber Abaci (1202 AD).

What’s far more important is that he popularised the Hindu-Arabic numeral system in Europe. Up to this, Europeans grappled with Roman Numerals. Imagine calculating XXV percent tax on MDCXXVI dinars? The adoption of the Hindu-Arabic system greatly simplified banking, trade and many calculations.

Anyway, the Fibonacci series was known to Indian mathematicians over 1,000 years before Fibonacci.

Illustrating that puzzles and recreational maths very often lead to fruitful seams of mathematics, Fibonacci introduced the sequence in the puzzle below. It’s solved by figuring out the pattern and then imagining the sequence running on into the future – an early example of mathematical modelling.

A man put a newly born pair (one male and one female) of rabbits in a field. After a month, the rabbits are mature to mate. After another month, they’ll give birth to one pair (male and female) of rabbits. How many rabbits will be present after 12 months (assuming this proceeds every month and no rabbits die or leave the field)?

Here’s another puzzle from Liber Abaci:

A man buys 30 live birds that include partridges, pigeons and sparrows for 30 dinars. A partridge costs three dinars, a pigeon costs two dinars, and two sparrows cost one dinar. How many birds of each kind did he buy?

It might be easier to consider 30 birds for €30 and a partridge costs €3, a pigeon costs €2, one sparrow costs 50c.

Solution: The girl’s birthday is on 31 December when she turned 23.

We spoke on 1 January and two days before 30 January she was 22.

On 31 December this year she will turn 24.

On 31 December next year she will turn 25.

Come back tomorrow at 7.30pm for the answers to today’s puzzle.

The puzzles this week have been compiled by Eoin Gill and Colm Mulcahy of Maths Week Ireland / South-East Technological University (SETU).

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The Journal Team