WE’RE GETTING TO the end of Math’s Week… and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

The last straw

Martin Gardner (1914 – 2010), the great American populariser of mathematics, wrote a column called Mathematical Games for over 25 years and published over 100 books.

He introduced many new games and ideas and revealed the underlying mathematics in games, art and magic in an accessible way to a wide audience.

The Gathering4Gardner Foundation celebrates the legacy of Gardner and promotes interest in mathematics.

His birthday was 21 October, and around this time every year, around the world, devotees organise Celebration of Mind events to promote logical thinking and having fun with puzzles of all sorts.

An event will take place this Sunday at the National Botanic Gardens, Glasnevin, in Dublin.

It starts at 12 noon and the event runs in conjunction with the annual pumpkin festival.

The lively Maths Week team will present family entertainment, games, puzzles and challenges for all ages.

Today’s puzzles were among Martin Gardner’s favourites.

A. It is easy to arrange three objects of the same shape and size so that each one touches the other two. Can you arrange four coins of the same size so that each coin touches the other three?

B. Arrange five coins of the same size so that each coin touches the other four.

C. Arrange six straws of the same size so that each straw touches the other five. The straws must not be bent or broken.

D. (The Last Straw) Is it possible to arrange seven straws of the same size so that each touches the other six? The straws must not be bent or broken.

Friday’s puzzle: The answer

1. Scan one package of apples and 100 tins of bananas.

This separates the two expenses sufficiently that anyone can read off the individual costs easily.

If the answer is €13.76 then the 76 cents must be the cost of a package of frozen apples, and the €13 must be the cost of 100 tins of bananas, so each tin of bananas costs 13 cents.

Similarly, if the answer is €52.20 then the 20 cents must be the cost of a package of frozen apples, and the €52 must be the cost of 100 tins of bananas, so each tin of bananas costs 52 cents.

2. Scan one package of apples, 100 tins of bananas, and 10,000 jars of picked clementines (we did say the scanner was huge!).

This also separates the three expenses sufficiently that anyone can read off the individual costs.

If the answer is €3287.55 then the 55 cents must be the cost of a package of frozen apples, €87 must be the cost of 100 tins of bananas, and €3200 must be the cost of 10,000 jars of pickled clementines. The individua costs of the tins of bananas and jars of clementines are 87c and 32c, respectively.

This shows how many numbers (with restrictions) can be coded in one number; in this case the individual numbers are positive whole numbers less than 100.

This concept has applications in computer and information science and…

Check back tomorrow for the answers to today puzzle. 

The Maths Week puzzles this year are presented by Colm Mulcahy, professor emeritus of Mathematics at Spelman College, USA, and adjunct professor with Calmast at South East Technological University. Colm is chairperson of the Martin Gardner Foundation USA, and the curator of the website mathsireland.ie