Making a biased coin fair.

In how many ways can you make it up the stairs?

This week would have been the 100th birthday of Martin Gardner, who is deservedly credited with turning on several generations of people worldwide to the pleasures of maths! To mark the occasion here are some favourite puzzles that, apart from being fun, also lead to some serious maths.

Making a very special number out of primes.

A life insurance agent knocks on a door. A woman answers and he tries to sell her a policy. He asks her how many children she has and their ages. She replies: "I have three children, but I will not even listen to your sales pitch unless you guess their ages..."

Find the number x that satisfies two interesting properties.

A mad robot sets off on a journey mindlessly following a set of instructions. Where will it explode?

Sharpen that wooden stake!

Which gives a tighter fit: a square peg in a round hole or a round peg in a square hole?