Samantha from Hamlin sent us her work on this problem. She found that it is possible to choose cards so that all of the boxes can be filled in. In fact, she chose cards so that she could fill in all of the boxes using a 1x1 square! Here is her example :

Has all equal angles 
Has rotational symmetry 
Has more than 1 axis of symmetry 
Has area of 1 unit 
Has more than 2 equal angles 




Has more than 1 right angle 




Has more than 2 equal sides 




Has 2 pairs of parallel sides 




Well done to Christine, Peter, Rebecca and Josh from Ely St John's School who found two more ways to choose cards so that all the boxes could be filled in. They decided to use rectangles as well as squares. Here is one of their solutions.

Has more than 1 axis of symmetry 
Has all equal angles 
Has more than 2 equal angles 
Has 2 pairs or parallel sides 
Has more than 1 right angle 
square 
square 
square 
square 
Has more than 2 equal angles 
square 
square 
square 
square 
Has area of 1 unit

square 
square 
square 
square 
Has area of 2 units

rectangle 
rectangle 
rectangle 
rectangle 
George found that it is possible to choose cards so that none of the boxes can be filled in. Here's the example he sent us:

More than one axis of symmetry 
Just two pairs of parallel sides 
Rotational symmetry 
All angles equal 
Just one axis of symmetry 




Just one pair of parallel sides 




Just two equal angles 




One right angle 




If anyone has had a go at these questions using the
triangle cards, do send your solutions to
the secondary team.