Proof by contradiction is when we assume that what we want to prove is not true, and then show that the consequences of this are not possible. The tasks below offer opportunities to use proof by contradiction. They form part of our Mastering Mathematics: Developing Generalising and Proof Feature.
problem
Play to 37
Age
7 to 11
Challenge level
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.