### 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?

# Concrete Wheel

##### Age 11 to 14 Challenge Level:

Alan Schoenfeld reports that:

Some people think that the room will go (almost) instantaneously dark as the wheel first passes the window, that it will stay dark for a short while and then go (almost) instantaneously light as the wheel leaves.

Others think that the room will go (almost) instantaneously dark as the wheel first passes the window, that it will stay dark for a relatively long time and then go (almost) instantaneously light as the wheel leaves.

Others think that the room darkens slowly, as though a large curtain is being pulled, more or less horizontally (from left to right), or diagonally (from the top left corner), or vertically downwards, as in the sketches below:

The room then stays dark for a short /long period of time, after which it lightens in a way that is complementary to the way it darkened.

What do you think?