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

Some people seem to be great at problem solving, while some of us never seem to know where to start. The good news is that problem-solving skills – like other skills – can be developed.

Most of what are referred to as problems in maths class are in fact exercises, practicing techniques learned earlier. ‘Problems’ for our purposes means ‘challenges’ where it isn’t immediately obvious how to find the solution.

A good way to hone your problem-solving skills is with puzzles. Puzzles are generally problems set for recreation. We have a good feeling of “I did it” after solving a puzzle. But if, on top of that, we also focus on “how I did it”, we can develop powerful generic skills.

Over the next seven days, we’ll present puzzles for you to enjoy and which will improve your skills.

Before we begin, here are some tips from the experts:

• We need to approach problem solving in the right frame of mind.
• Don’t be afraid to make mistakes – look at them as the start of learning.
• Of course, you have limited time to spend on a puzzle, but don’t give up too easily.
• And finally, be reflective. Think about what you’re doing, where is it getting you? What strategies have been effective?

PUZZLE 1: Trial and improve

There are generic strategies that people use without much awareness. Trial and error is a great strategy. It gets us stuck in straight away and we might see other options when we’re working.

We need to be smart though, we can’t try the same thing again and again and expect a different outcome. So we must trial and improve. Where did we go wrong the last time How can we try something new this time?

We’ll start with a series of puzzles that only require basic arithmetic: plus, minus, multiplication and division (+, – , *, / ).

We call this the number plate game.

Take the digits of each of the car registration numbers (not the year) below and see if using each digit once – and only once – and any of the basic operators (+, – , *, / ) as often as you like with as many brackets as you need, can you reach 24 for every one? 

• 221 G 12345
• 221 D 35210
• 221 W 23578
• 221 C 85372
• 221 LH 69996
• 221 L 1346 

Obviously, trial and error is a good starting strategy. But you might see a 6 and knowing that 6*4 = 24, see if you can make a 4. Similar with an 8 and 3.

This is an example of identifying and aiming for an intermediate point rather than the endpoint – another useful strategy.

Puzzles compiled for The Journal by Eoin Gill of Maths Week Ireland / Waterford Institute of Technology.