### 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?

# Framed

##### Age 11 to 14Challenge Level

Seven small pictures, all square or rectangular, with sides measuring a whole number of inches and each with a different area, have frames exactly one inch wide.

In each case the area of the frame is either the same as the area of the picture or a multiple of it.

The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches.

Find the dimensions of the pictures, show how they fit together to make a rectangle, and find the width of the rectangle.