You may also like

problem icon

All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

problem icon

Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

problem icon

The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

Farmers Field

Stage: 3 Challenge Level: Challenge Level:1

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are expensive to build, so naturally the farmer wishes to build the shortest wall he can.

Can you prove that the shortest wall is always straight, whatever the shape of the original field? Or perhaps you can find a shape where the shortest wall isn't straight!