February 2003, Stage 2&3

Problems

Multilink Cubes

Stage: 2 Challenge Level:

If you had 36 cubes, what different cuboids could you make?

Three Cubed

Stage: 2 Challenge Level:

Can you make a 3x3 cube with these shapes made from small cubes?

Cereal Packets

Stage: 2 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Construct-o-straws

Stage: 2 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

Cubes Within Cubes

Stage: 2 Challenge Level:

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Cubic Conundrum

Stage: 2 Challenge Level:

Which of the following cubes can be made from these nets?

Playground Snapshot

Stage: 2 and 3 Challenge Level:

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Pretty Prism Perspective

Stage: 3 Challenge Level:

Try making 3D patterns in two dimensions with LOGO

Icosian Game

Stage: 3 Challenge Level:

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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. . . .

Cutting a Cube

Stage: 3 Challenge Level:

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Cubist Cuts

Stage: 3 Challenge Level:

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?