The Old Goats
A rectangular field measuring 17.5 metres by 10 metres has two posts 7.5 metres apart with a ring on top of each post. The posts are approximately 7 metres from the nearest corners as shown in the diagram. You have two quarrelsome goats and plenty of ropes which you can tie to their collars and you want them to be able to graze the whole field between them. How can you secure them, using the posts, so they can't fight each other, and how much rope is needed?
You may also like
All in the Mind
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Instant Insanity
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Is There a Theorem?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?