# Can you solve it? Are you in the smartest 1 per cent (of 13-year-olds)?

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 cm2.

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.

I’ll be back with the solutions at 5pm UK time.