When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?
Can you devise the most efficient strategy for finding the highest floor from which you can drop an egg safely?
In how many ways can I get upstairs?
How many different lengths is it possible to measure with a set of three rods?