### Purr-fection

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

### More Mods

What is the units digit for the number 123^(456) ?

### 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?

# Obviously?

##### Age 14 to 18 Challenge Level:

Find the values of $n$ for which $1^n + 8^n - 3^n - 6^n$ is divisible by 6.