MATHS WEEK STARTS today 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 seven days here. 

The 20th annual Maths Week Ireland starts today and runs until Sunday 19 October. 

For dedicated readers of The Journal, this means daily puzzles to exercise the grey cells.

By the end of Maths Week 2025, we expect to have reached an amazing cumulative figure of 5 million participants over the 20 years. 

Mathematical thinking goes beyond school maths and is useful for problem solving, even in everyday situations we mightn’t realise such as planning an event or holiday, decorating, shopping and saving and budgeting, of course.

The good news is that this ability can be learned and practiced – and puzzles are a great way to improve our mathematical thinking.

With that, it’s time for today’s tip:  

For decades there has been a battle in maths education over times tables. One side insists on the necessity of learning them by rote, while the other side believes that if pupils were equipped with a deeper understanding they could work out their arithmetic without the memory games.

Of course, like in many areas of life, the answer lies somewhere in between. In this battle, 11 and 12 times multiplication tables were a particular battleground. In fact, there is a neat trick for 11 times multiplication and because this is the 11th of the month I will share it with you.

To multiply a two-digit number by 11, keep the first and last digit and between them put the sum of the first and last digit.For example:

36 x 11 = 3 (3+6) 6 = 396

Pretty easy, but mind if you have to carry. Add the carried digit to the left – onto the first digit:

55 x 11 = 5(5+5)5 = 5(10)5 = 605

This technique can be extended to larger numbers. For example: 

426 x 11 = 4(4+2)(2+6)6 = 4686

3541 x 11 = 3(3+5)(5+4)(4+1)1 = 38951

Again, if you have to carry, working from the right, add to the digit on the left.

36835 x 11 = 3(3+6)(6+8)(8+3)(3+5)5 = 3(9)(14)(11)(8)5 = 405185

There are many more interesting and quirky things to discover in maths.

Today we present a selection of short puzzles to start off the week for The Journal readers.

Have a go each day, don’t worry if you can’t do them all or if you make mistakes. It is through mistakes that we learn.

1. Mental arithmetic: what is 45 x 11?

2. Mental arithmetic: what is 623 x 11?

3. What three digits when multiplied together give the same answer as when added
together?

4. What two numbers when multiplied together give the same answer as when added together?

5. Nora and Will collected some blackberries. Nora tells Will that if he gave her two blackberries, they would have the same amount. But if she gave him two berries he would have twice as much as her. How many blackberries did each have?

6. Mary was asked how much shopping her shopping costs. She replied, “Butter was €5.60, flour was €1.85 and eggs were €3.50.”

“No,” I said. “How much did it cost altogether?”

“€20”, she replied.

How many of each item did she buy?

7. One typist can type 40 words per minute and another can type 60 words per minute.
Together, how many words can they type in 10 minutes?

8. How long would it take the two typists from question 7 to type 600 words?

9. There are 8 black and 6 white socks in a drawer. How many would you have to pull
out at random to be certain of a matching pair?

10. Anne was four times as old as Brian 12 years ago. In 6 years’ time she will be twice
as old as Brian. How old are they now? 

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.