A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

This short question asks if you can work out the most precarious way to balance four tiles.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Which parts of these framework bridges are in tension and which parts are in compression?

Dmitri from Cork and others offered a neat way to visualise this process and to reason how one result leads to the next.

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.