### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Colourful Tiles

##### Stage: 3 Short Challenge Level:

Consider the colour at the top. There are $4$ different choices for this: red, yellow, green and blue. For the right hand colour, this can be any of the other $3$ colours that have not yet been used. The bottom colour can then be either of the other $2$ colours. The left hand part then has to have the remaining colour.

This means there are $4 \times 3 \times 2 \times 1 = 24$ different ways to paint all four sections. This means there are $23$ other ways to paint the tile.

This problem is taken from the UKMT Mathematical Challenges.