February 2003, Stage 3&4

Problems

Playground Snapshot

Age 7 to 14 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?

Cubes Within Cubes

Age 7 to 14 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?

Pretty Prism Perspective

Age 11 to 14 Challenge Level:

Try making 3D patterns in two dimensions with LOGO

Icosian Game

Age 11 to 14 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.

Marbles in a Box

Age 11 to 14 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Cutting a Cube

Age 11 to 14 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

Age 11 to 14 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?

Cubic Conundrum

Age 7 to 16 Challenge Level:

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

All in the Mind

Age 11 to 14 Challenge Level:

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?

Excel Technique: LOOKUP Functions

Age 11 to 16 Challenge Level:

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

Excel Interactive Resource: Equivalent Fraction Bars

Age 11 to 16 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Excel Investigation: Happy Numbers

Age 11 to 16 Challenge Level:

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

In a Spin

Age 14 to 16 Challenge Level:

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Plum Tree

Age 14 to 18 Challenge Level:

Label this plum tree graph to make it totally magic!

Magic Caterpillars

Age 14 to 18 Challenge Level:

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.