### 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...

# Painted Purple

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

The solution depends on how the cube is painted.

If you paint the large cube so that two of the small corner cubes have their three painted faces all painted the same colour, then $12$ of the small cubes will have at least one red face and also at least one blue face.

If you paint the large cube so that no small corner cube has all three of its painted faces painted the same colour, then $16$ small cubes will have at least one red face and one blue face.

This problem is taken from the UKMT Mathematical Challenges.