# To Iff or Not to Iff?

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.

### River Crossing

##### Age 11 to 18Challenge Level
There is nothing half so much worth doing as simply messing about in boats...

### Iffy Logic

##### Age 14 to 18Challenge Level
Can you rearrange the cards to make a series of correct mathematical statements?

### IFFY Triangles

##### Age 14 to 18Challenge Level
Can you prove these triangle theorems both ways?

### The Tour De Clochemerle

##### Age 14 to 18Challenge Level
Can you work out where these 5 riders came in a not-quite-so-famous bike race?

### Iff

##### Age 14 to 18Challenge Level
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

### Mind Your Ps and Qs

##### Age 16 to 18Challenge Level
Sort these mathematical propositions into a series of 8 correct statements.