List

Are You Sure?

Image
15053 Header


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
problem

Maxi Pyramid

Age
11 to 16
Challenge level
filled star empty star empty star
What is the largest number you can obtain at the top of this pyramid?
Positive Differences
problem

Positive Differences

Age
11 to 16
Challenge level
filled star empty star empty star
Can you fill the circles with the numbers 1 to 6?
Sliding Rectangles
problem

Sliding Rectangles

Age
11 to 16
Challenge level
filled star empty star empty star
Which of the two rectangles has the greater area?
11x11 square
problem

11x11 square

Age
11 to 16
Challenge level
filled star filled star empty star
Here's a neat trick you can do with an 11 by 11 square...
River Crossing
problem

River Crossing

Age
11 to 18
Challenge level
filled star empty star empty star
There is nothing half so much worth doing as simply messing about in boats...
Isosceles Seven
problem
Favourite

Isosceles Seven

Age
14 to 16
Challenge level
filled star empty star empty star
Is it possible to find the angles in this rather special isosceles triangle?
The Tour de Clochemerle
problem

The Tour de Clochemerle

Age
14 to 18
Challenge level
filled star empty star empty star

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

Iffy logic
problem
Favourite

Iffy logic

Age
14 to 18
Challenge level
filled star empty star empty star
Can you rearrange the cards to make a series of correct mathematical statements?
IFFY triangles
problem

IFFY triangles

Age
14 to 18
Challenge level
filled star empty star empty star

Can you prove these triangle theorems both ways?

Iff
problem
Favourite

Iff

Age
14 to 18
Challenge level
filled star filled star empty star
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?