Image

Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs. There are also a selection of "dodgy proofs" where your challenge is to find out where the logic breaks down.

Plus magazine has a selection of interesting articles about proofs here.

problem

### What does it all add up to?

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

problem

### Difference of odd squares

$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?

problem

### Impossible sums

Which numbers cannot be written as the sum of two or more consecutive numbers?

problem

### Adding odd numbers (part 2)

Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?

list

### KS5 Proof shorts

Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).

problem

Favourite

### Direct logic

Can you work through these direct proofs, using our interactive proof sorters?

*We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.*