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. 

Is there anything we take for granted more than numbers?

Imagine if we still had Roman numerals, how would you calculate a tip in a restaurant.

How would you calculate IX% VAT?

In ancient Rome or mediaeval Europe such everyday calculations were performed by specialists. A man called Leonardo of Pisa was largely responsible for the introduction of the Indo-Arabic numerals, 1-9 and 0, to Europe.

He did this through his book Liber Abaci -which is translated to English as Book of Calculations – and which earned him the name Fibonacci. (We have met Fibonacci before with his puzzle of the rabbits).

Fibonacci posed other puzzles that were instructional in maths learning, as well as being entertaining. Try them: 

1. A certain man buys 30 birds – sparrows, turtle-doves and doves – for 30 pounds.

Three sparrows cost 1 pound, two turtle-doves cost 1 pound and a dove costs 2 pounds.

It is required to find how many birds he buys of each kind. That is quite a tricky problem, especially as Fibonacci solved it without formal algebra.

2. I bought oranges, bananas and apples. Oranges cost €1.50, bananas cost €1 and apples cost 60c. I got 10 pieces of fruit for €10. How many of each did I buy?

3. Bill and Ben were discussing their pocket money.

“I have 10 coins,” said Bill.

“So have I,” said Ben.

“I have only two denominations,” said Bill.

“So have I,” replied Ben.

“That’s quite a coincidence, I have €1.85,” observed Bill.

“So have I,” exclaimed Ben. “I wonder if we have the exact same coins?”

It turned out they had only one denomination in common.

What were the other two denominations?

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Tuesday’s puzzle: The answers

16 starters, 23 main courses and 25 desserts.

Construct a Venn diagram of three overlapping circles representing each course.

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Maths Week: Your Saturday puzzle

Enter the information we have.

Note that 3 people ordered only one course but nobody ordered only starter or only a main course, so 3 people ordered only dessert.

At this stage we don’t know how many ordered all three courses. The number of people so far sums to 23 and as there are 30 people altogether, 7 people must have ordered all three courses.

From the Venn diagram we sum the total in each circle to determine the number of each
course.

Starter 7+5+4 = 16

Main course 7+5+11 = 23

Dessert = 11+7+4+3 = 25

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.