**The test given to the UK’s maths prodigies**

Today you are pitting yourselves against the best 13-year-old mathematicians in the UK.

The questions below are taken from last week’s Junior Mathematical Olympiad, a competition aimed at children up to Year 8 (in England) who score in roughly the top half per cent of mathematical ability.

The competition is a two hour paper, split into two sections. I’ve chosen three questions from the more challenging section, presented in increasing level of difficulty.

1. *In this word-sum, each letter stands for one of the digits 0–9, and stands for the same digit each time it appears. Different letters stand for different digits. No number starts with 0.*

*Find all the possible solutions of the word-sum shown above.*

2*. In the diagram below, a quarter circle with radius 3cm is positioned next to a quarter circle with radius 4cm.*

*What is the total shaded area bounded by the blue lines, in cm ^{2}.*

3. *An equilateral triangle is divided into smaller equilateral triangles*

*The figure on the left shows that it is possible to divide it into 4 equilateral triangles. The figure on the right shows that it is possible to divide it into 13 equilateral triangles.*

*What are the integer values of n, where n > 1, for which it is possible to divide the triangle into n smaller equilateral triangles?*

The Junior Mathematical Olympiad is run by the UK Mathematics Trust, a fantastic organisation that promotes maths in school by, among other things, organising national competitions.

In April, 272,263 children took the UKMT’s Junior Mathematical Challenge, which is for children in Year 8 or below (England), S2 or below (Scotland) or Year 9 or below (Northern Ireland).

The 995 kids with highest marks – that’s the top 0.37 per cent – qualified to sit the olympiad last week.

Source: The Guardian