In this feature you will find a selection of problems that will require you to reason logically. You will also be introduced to the symbols $\implies$ and $\iff$ and be challenged to use these to create true statements.

The live problems will be open for solutions until Monday 16 May.

Plus magazine has a selection of interesting articles looking at logic, mathematical logic, its role in computer science and the philosophy of maths, and on how it's being used in applications.

Challenge Level

There is nothing half so much worth doing as simply messing about in boats...

Challenge Level

Can you rearrange the cards to make a series of correct mathematical statements?

Challenge Level

Can you prove these triangle theorems both ways?

Challenge Level

Can you work out where these 5 riders came in a not-quite-so-famous bike race?

Challenge Level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Challenge Level

Sort these mathematical propositions into a series of 8 correct statements.