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?

Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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

Stage: 3 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.