Winning Maths
How to win at Maths
Solve the problems on this page
Send your answers to the address below
Join the Mathematical Talent Search
Learn new problem-solving skills
Expand your career horizons
Earn your place in the South African team
Mathematical Talent Search

Problem 1

Two circles intersect with their centres 6cm apart. Circle A has area 50cm2 and Circle B has area 30cm2. Find the difference in area between the blue and the red shaded regions.

Problem 2

Towns A, B, C, D, E, F, G and H lie on a straight road. The table shows the distances between pairs of towns (for example, D is 19km from G). Fill in the distances in the rest of the table.

Problem 3

A triangle is made up of ten cents. What is the smallest number of coins which must be moved to turn the triangle upside-down?

Problem 4

In the diagram, three squares are shown, all containing the star. Altogether, how many squares containing the star can be found in the diagram?

Problem 5

Twenty postage stamps are joined together as shown. In how many different ways can three postage stamps, joined together along their edges, be torn from the sheet?

Problem 6

Twenty-one gas cylinders are to be loaded onto three trucks. Seven are full, seven are half-full and seven are empty. A full cylinder weighs 50kg and an empty cylinder weighs 20kg. How should they be loaded onto the trucks so that each truck is carrying the same weight?
The Talent Search is a free course in problem solving, open to South African pupils from Grade 8 to 12. It aims to develop the mathematical skills of its participants, and eventually to identify teams of young mathematicians to represent South Africa at the International Mathematical Olympiad and Pan African Mathematics Olympiad.

To enter, send your name, address, school and grade, to:

   Mathematical Talent Search
   Department of Mathematics
   University of Cape Town
   7700 Rondebosch