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?

Largest Number

Stage: 3 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like. You can only use each digit once.
For example: 34 x 2 = 68 or 3 + 4 2 = 19

(We will publish the ten highest numbers sent in, as long as you show how got the answer)