### Lastly - Well

What are the last two digits of 2^(2^2003)?

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

### Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

# Even So

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

Find some triples of whole numbers $a$, $b$ and $c$ such that $a^2 + b^2 + c^2$ is a multiple of 4. Is it necessarily the case that $a$, $b$ and $c$ must all be even? If so, can you explain why?