### 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?

### Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

### 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.

# Concrete Wheel

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

Imagine that you are sitting in a room at ground level, facing a floor-to-ceiling window which is 20 feet by 20 feet.

A huge concrete wheel, 100 miles in diameter, is rolling down the street and is about to pass right in front of the window, from left to right.

The centre of the wheel is moving to the right at 100 miles per hour.

What does the view look like, from inside the room, as the wheel passes by?

This problem appears in "Mathematical Thinking and Problem Solving", edited by Alan Schoenfeld and published by LEA press.