### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

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

# Elf Suits

##### Stage: 2 Challenge Level:

Mrs Claus made four of the workshop elves new suits for Christmas.

Each suit had matching trousers, waistcoat, jacket and hat.

One suit was all red, one was all green, one was all yellow and one was all blue. The elves were delighted with their presents, but decided it would be fun to wear a different outfit every day for as many days as possible. So they agreed to swap around parts of their suits until they ran out of new combinations.

How many days did their fun last?

At the end of 2015 Lucy and Reece from Eskdale Academy solved the problem and then asked

The answer (?) takes into account all combinations of clothing but it does not take into account whether or not you put the same colours on the elves on the same day.  We thought that it wouldn't work because there is only one item of each colour, e.g. one pair of red trousers.  Also, is there a system to find out exactly what the elves wore each day?

So, take the challenge further and make some suggestions to Lucy and Reece.