IN HONOUR OF Maths Week, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

The Basic Operators

With the development of counting came the need to add, subtract, divide and multiply numbers. These are the basic operations of arithmetic, and the word arithmetic comes from the Greek word arithmos, meaning “number”.

Ancient civilisations such as the Sumerians, Babylonians, and Egyptians used early forms of arithmetic to keep records of trade, land, taxes, and food production.

Our own ancient ancestors would have used their own form of arithmetic to build amazing structures such as Newgrange.

We still use arithmetic for our daily problem-solving activities, but it also underpins higher branches of math like algebra and geometry. While we mostly use the four basic operations there are also more complex operations such as powers and roots. In arithmetic we use standard symbols for the operators, for instance: + – ÷ x and = .

This makes it easier and quicker to write down our work. It is essential that these are standard symbols, so they are clearly understood by others anywhere in the world. The use of symbols is a feature of maths and while they are used for efficiency and clarity, they do often add an extra layer of difficulty.

Here are some arithmetic puzzles that require only the four basic operators.

1. What positive whole numbers divide evenly into 24? (that is without leaving a remainder)
2. Can you make 24 out of the following sets of numbers using just the four basic operators and all of the digits.
   a) 1,2,3,4 example: 1 x 2 x 3 x 4 = 24
   b) 7,9,6,2
   c) 5,5,2,1
3. Using each of the four digits 2,4,6,8 once and only once and the four basic operations (+ – ÷ x), can you make
   a) 24
   b) 20
   c) 13
   d) 23
4. Before calculators, computers and smartphones arithmetic, mental and on paper, was a very important skill. The following is a typical problem that primary school children were expected to solve in bygone days.
   A farmer rents a field of 3 acres, 3 roods and 21 perches at a rate of £4 6s 8d per acre. How much does he pay for the field?
   Of course, you have to know that 1 acre = 4 roods and 1 rood = 40 perches, £1 (pound) = 20s (shillings), 1s = 12d (pence).

Sunday’s puzzles: The answers

1. 1, 3, 5, 7, 9, ? 11 add 2 each time
2. 2, 3, 5, 7, 11, ? 13 (prime numbers)
3. I, IV, IX, ? XVI 1,4,9,16 (Square numbers)
4. 1, 1, 2, 3, 5, ? 8 Fibonacci Series: each term is the sum of the two previous terms.
5. 1, 3, 6, 10, 15, ? 21 Add 2, 3, 4, 5, 6… (Triangular numbers)
6. 1, 3, 7, 15, 31, ? 63 Double the previous number and add 1, or for each term, n is 2 n – 1.
7. 89, 55, 34, 21, ? 13 Fibonacci series backwards
8. ¼, ½, ¾, ? 1 Add ¼ each time
9. 1, 2, 6, 24, 120, ? 720 1, 2×1, 3x2x1, 4x3x2x1, 5x4x3x2x1, 6x5x4x3x2x1 (Factorials)
10. 13, 3, 5, 4, 4, ? 3 Letters in each number: one, two, three, four, five, six

Come back tomorrow at 7.30pm for the answers to today’s puzzle. 

The puzzles this week have been compiled for The Journal by Eoin Gill of Maths Week Ireland and South-East Technological University (SETU).