Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Inside a Parabola

Age 14 to 16 ShortChallenge Level

The points where the parabola $y=k^2-x^2$ crosses the coordinate axes are joined to form a triangle.

The area of the triangle is 64 square units. What is the value of $k$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.