Puzzle

An unusual sales pitchA 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..."
Mystery number: hint
Mystery numberFind the number x that satisfies two interesting properties.
Mad robotA mad robot sets off on a journey mindlessly following a set of instructions. Where will it explode?
Kill the vampireSharpen that wooden stake!
Hint for the peg and hole puzzle
Round peg in square hole or square peg in round hole?Which gives a tighter fit: a square peg in a round hole or a round peg in a square hole?
Jail breakHow many prisoners escape after visits from wardens?
Prime birthday

The n-th birthday of a very famous mathematician coincides with a year that corresponds to the (n+1)st prime number. Who is this mathematician?
2011 in foursWrite the number 2011 using only the digit 4 and the operations of addition, subtraction, multiplication, division, exponentiation, taking a square root and factorial. You can use any number composed of the digit 4, even if it's decimal, so 44 and 44.44 are both allowed. You're also allowed to use brackets.
League table teasersFootball tables have been the basis of many a brainteaser over the years. These two puzzles ask you to work out what the scores were in all matches played so far this season.
A hint for the cheese cutting puzzle