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.

Challenge Level

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

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Can you fill the circles with the numbers 1 to 6?

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Which of the two rectangles has the greater area?

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Here's a neat trick you can do with an 11 by 11 square...

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

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

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

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

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Can you prove these triangle theorems both ways?

Challenge Level

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