### Diggits

Can you find what the last two digits of the number $4^{1999}$ are?

### Like Powers

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

### Two Many

What is the least square number which commences with six two's?

# Maundy Money

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

Every Maundy Thursday, the reigning monarch distributes 'Maundy money' to equal numbers of men and women.

One year at Newcastle 64 men and 64 women each received 64p, one penny for each year of the Queen's life.

Written as a power of 2, what was the total amount distributed in pence?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.