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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Are You Sure?

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Maxi Pyramid

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River Crossing

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Isosceles Seven

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The Tour De Clochemerle

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Iffy Logic

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Iff

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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.

Age 11 to 16

Challenge Level

What is the largest number you can obtain at the top of this pyramid?

Age 11 to 18

Challenge Level

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

Age 14 to 16

Challenge Level

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

Age 14 to 18

Challenge Level

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

Age 14 to 18

Challenge Level

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

Age 14 to 18

Challenge Level

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