Reasoning, convincing and proving

Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?

Weekly Problem 8 - 2016
Can you work out the size of the angles in a quadrilateral?

In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

What is the largest number Sophie can use to have seven positive integers with a mean of 7?

Sequences of multiples keep cropping up...

Play around with the Fibonacci sequence and discover some surprising results!

Can you explain what is going on in these puzzling number tricks?

Can you find the areas of the trapezia in this sequence?

This task combines spatial awareness with addition and multiplication.