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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
Favourite
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
Favourite
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
Favourite
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?