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

Day Two – Patterns and Relationships

We humans seem to have an innate ability to perceive quantities in small sets of objects. Numbers allow us to count and communicate precise amounts, enabling us to consider much larger quantities.

Numbers were developed sometime in prehistory, and this was surely one of the great advances of civilisation.

The Ishango Bone, which appears to have been used for counting and was found in the Democratic Republic of Congo, dates back some 20,000 years. The Sumerians, around 6,000 years ago developed a numerical system in base-60. As we have 10 fingers to count with, the decimal system (base-10) seems obvious to us, but it did not appear until about 5,000 years ago in ancient Egypt.

The earliest numbers were the counting numbers: 1, 2, 3, 4, and so on.

Fractions evolved to allow quantities such as land or goods to be divided, with a half expressed as 1 divided by 2 (½) and a quarter as 1 divided by 4 (¼). Later on, these fractions were expressed as decimals (1/2 = 0.5 and 1/4 = 0.25). Throughout the years other forms of numbers were developed.

The Romans used a system of numerals that was very cumbersome for calculations. Meanwhile, in India, they had a decimal place-value system that included zero. This Indian system spread to the Islamic world and reached Europe in the Middle Ages. As number systems evolved, so too did arithmetic, geometry, and algebra.

Maths is about patterns and relationships. Can you work out the patterns in each of the number series below and find the next term for each?

1) 1, 3, 5, 7, 9, ?

2) 2, 3, 5, 7, 11, ?

3) I, IV, IX, ?

4) 1, 1, 2, 3, 5, ?

5) 1, 3, 6, 10, 15, ?

6) 1, 3, 7, 15, 31, ?

7) 89, 55, 34, 21, ?

8) ¼, ½, ¾, ?

9) 1, 2, 6, 24, 120, ?

10) 3, 3, 5, 4, 4, ?

Saturday’s puzzles: The answers

1. 6 (there are 6 halves in 3)
2. 83.33p
3. (a) costs €2 (b) costs €2.10
4. (b) as (a) would cost €24.60
5. €3
6. (b) ¾

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).