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 Logiclive

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?