Are You Sure?


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.

 

Maxi Pyramid 

Age 11 to 16
Challenge Level
What is the largest number you can obtain at the top of this pyramid?

Positive Differences 

Age 11 to 16
Challenge Level
Can you fill the circles with the numbers 1 to 6?

Sliding Rectangles live

Age 11 to 16
Challenge Level
Which of the two rectangles has the greater area?

11x11 Square 

Age 11 to 16
Challenge Level
Here's a neat trick you can do with an 11 by 11 square...

River Crossing 

Age 11 to 18
Challenge Level
There is nothing half so much worth doing as simply messing about in boats...

Isosceles Seven 

Age 14 to 16
Challenge Level
Is it possible to find the angles in this rather special isosceles triangle?

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?

Iffy Logic live

Age 14 to 18
Challenge Level
Can you rearrange the cards to make a series of correct mathematical statements?

IFFY Triangles 

Age 14 to 18
Challenge Level
Can you prove these triangle theorems both ways?

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?