### Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

### Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

### Mod 7

Find the remainder when 3^{2001} is divided by 7.

# Remainder Hunt

##### Age 16 to 18 Challenge Level:

What are the possible remainders when the $100^{th}$ power of an integer is divided by $125$?