List

Are you sure?

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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.

problem

Maxi pyramid

Age

11 to 16

Challenge level

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

problem

Positive differences

Age

11 to 16

Challenge level

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

problem

Sliding rectangles

Age

11 to 16

Challenge level

Which of the two rectangles has the greater area?

problem

11x11 square

Age

11 to 16

Challenge level

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

problem

River crossing

Age

11 to 18

Challenge level

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

problem

Isosceles seven

Age

14 to 16

Challenge level

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

problem

The Tour de Clochemerle

Age

14 to 18

Challenge level

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

problem

Iffy logic

Age

14 to 18

Challenge level

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

problem

IFFY triangles

Age

14 to 18

Challenge level

Can you prove these triangle theorems both ways?

problem

Iff

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?