Volume 32 Issue 05 - 27 March 2020

Maths Matters

A simple numeracy problem that can keep your mind active when staying inside is the Four 4s puzzle. All you need is a piece of paper and a pen. If you want to have a more structured set out for your answers, then there are many answer templates available online that can be freely downloaded.

Image courtesy of Joshua Combes - CAPA Coordinator

The task is to form a mathematical expression for each whole number from 1 to 100 using four repetitions of the digit 4, as well as the four mathematical operations of addition, subtraction, multiplication and division. For example, some ways to calculate the number 16 could be

4 + 4 + 4 + 4 = 16

4 x 4 - 4 + 4 = 16

4/4 x 4 x 4 = 16

There are also many variations of the game such as allowing powers, square roots, cubed roots, percentages, reciprocals and the decimal point. Some simple variations include:

Concatenation: This means that you can join two of the 4 digits to make 44,
Brackets: Multiple sets of brackets can be used to change the order of operations by calculating the answer inside the brackets first,
Factorial notation. A factorial uses the ! symbol such that 4! = 4 x 3 x 2 x 1 = 24

Other alternatives to the puzzle could be to find the values using the fewest number of 4s or using five 5s, six 6s, or so on. Different challenges could be to change the target values, such as only finding the expressions for 0 to 20, or -10 to +10. To simplify the puzzle for younger kids, they could have a competition to see who can be the first to calculate any ten different whole numbers using the four 4s.

This puzzle could be something for you to do on your own or as a competition with family members. My Year 7 class last year enjoyed when I set them this puzzle after we had completed the classwork on a Friday afternoon - especially when I let them use calculators to find those last few elusive numbers!

Michelle Parker - Mathematics Teacher