MATHS WEEK DRAWS to a close today and over 500,000 people have been recorded engaging across the island this year in schools, educational and cultural venues – even on the streets and in parks- and as here, online.

Maths for All is the guiding principle and we have reached many under-served groups, promoting a positive attitude towards maths.

What is maths? Is it about numbers, algebra, geometry, or patterns? All of these, and a lot more. We have learned this week that maths is not always about numbers.

Throughout history, it has helped us to understand the world in which we live, and make predictions about the future. We are getting better at it, because of perseverance, hard work and ingenuity. The occasional “Aha, NOW it makes sense” helps, and as a result, we can predict the tides, the weather and the stock market with varying degrees of accuracy.

Maths is also one the key ingredients that makes modern technology, electronic communication, and the secure online commerce possible. Without it, say goodbye to your apps and phone and safe click purchases.

Numbers can give a sense of worth, indeed we sometimes we put too much trust in mere
numbers. Think of sports teams’ ratings and ranking, body mass index, or the chance of rain tomorrow. Some things are too complex to summarise in a single number, no matter how tempting that may be.

Maths (and astronomy and physics) arose because of insatiable human curiosity about the world around us. Why do we see recurring patterns at night (such as a full moon, roughly every four weeks), or during the day (the midday height of the sun, which in turn follows an annual cycle of highs and lows)? It took a long time until dedicated people figured all of that out. We saw (on Wednesday) that new mathematical ideas can find important (and unforeseen) practical applications many years later. There are many examples in the history of maths.

On a more mundane level, some people love challenges and puzzles (and word play),
regardless of any obvious utility, even if we often get stuck trying to solve them. Then there is the enduring popularity of the Rubik’s cube, Sudoku and Wordle (and the Irish version of the latter, Fochach). Engaging with such things sharpens the mind, engaging with such things sharpens the mind, especially useful, as we get older.

Can five coins all touch each other? How about seven straws? (see yesterday’s problem). Can you determine two unknown prices by making a single purchase and getting only the total bill? (see Friday’s problem). Brain-teasers about ages are as old as the hills (see Monday). Why does the bottom card of a packet of 11 cards come to the top if we spell out the name of any Irish president? (See Thursday). Those coins and straws challenges were popularised over 50 years ago by Martin Gardner, an American writer who loved all sorts of puzzles (and word play). About 40 of the 100 books he wrote were devoted to brain-ticklers.

He had a huge following and influenced several generations of people young and old, and
the intriguing questions he asked still delight readers today. Why does a mirror reverse the image left and right but not up and down?

At any age, we can benefit from doing puzzles and developing problem-solving strategies
that can be used in many areas of our lives. Puzzles are also a great way to draw in many
children: kids are naturally curious. Start with something easy, and work up to harder
questions. Don’t worry about whether there might be more than one answer, or no answer at all! Encourage effort and perseverance.

More about Maths Week at www.mathsweek.ie

Saturday’s puzzle: The answer 

A. Four coins

B. Five coins

C. Six straws

D. Seven straws

Note that the solutions for C and D take advantage of the fact that the straws have ends. Imagine infinitely long straws; is it possible to arrange six or seven of those so that each one touches all of the others?

This problem with seven straws is very difficult and no solution was known until 2013. That was found by means of a computer search of the possible solutions of the system of equations representing cylinders. One realization of seven (potentially) infinite mutually touching cylinders

One realization of seven (potentially) infinite mutually touching cylinders (by Bozóki, Lee & Rónyai, 2013). Photo by Colm Mulcahy

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