## Problems

##### 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?

##### 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?

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

Try making 3D patterns in two dimensions with LOGO

##### 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.

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

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

##### 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?

##### 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?

##### Age 7 to 16 Challenge Level:

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

##### 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?

##### Age 11 to 16 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

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

##### 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.

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

Label this plum tree graph to make it totally magic!

##### Age 14 to 18 Challenge Level:

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

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