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.

UPDATE: The solutions can now be read here.

PLEASE NO SPOILERS

In other exciting puzzle news, The Guardian has become the first newspaper to publish sandwich sudoku, the brilliant new sudoku variant I wrote about in this column in May. The puzzle now appears every Saturday in the print edition.

Thanks to the UK Mathematics Trust for this week’s questions.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of Football School, a book series for 7 to 12 year olds that opens up the curriculum through football. Football School Star Players: 50 Inspiring Stories of True Football Heroes is just out. It profiles 50 footballers who show that football can be a force for good both on and off the pitch.