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Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs.

The last day for sending in your solutions to the live problems is Monday 31 January.

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

problem

### Three consecutive odd numbers

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

problem

### Adding odd numbers

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

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

### Different Products

Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What 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?

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