Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

Scratch Cards

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Factoring a Million

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Flora the Florist

Age 14 to 16 ShortChallenge Level

Flora the florist has $24$ white, $42$ red and $36$ yellow roses.

What is the greatest number of identical bunches she can make that uses all of the flowers?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.