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In this feature you are invited to explore a variety of problems, and are then asked to construct convincing arguments to explain what you have discovered. You will also be introduced to the symbols $\implies$ and $\iff$ and be challenged to use these to create true statements.

The last day for sending in your solutions to the live problems is Monday 16 May.

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### River Crossing

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

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Favourite

### Isosceles Seven

Is it possible to find the angles in this rather special isosceles triangle?

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### The Tour de Clochemerle

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

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Favourite

### Iffy logic

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

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Favourite

### Iff

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