Weekly Problem 3 - 2012

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Weekly Problem 11 - 2012

A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?

Find the length along the shortest path passing through certain points on the cube.

The diagram shows two semicircular arcs... What is the diameter of the shaded region?

Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

This quadrilateral has an unusual shape. Are you able to find its area?

Weekly Problem 10 - 2010

Can you calculate the length of this diagonal line?

Weekly Problem 19 - 2010

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Weekly Problem 3 - 2011

What does Pythagoras' Theorem tell you about the radius of these circles?

How does the perimeter change when we fold this isosceles triangle in half?

Weekly Problem 20 - 2011

What is the perimeter of this unusually shaped polygon...

Weekly Problem 5 - 2013

The diagram shows 8 shaded squares inside a circle. What is the shaded area?

Weekly Problem 14 - 2014

Triangle T has sides of lengths 6, 5 and 5. Triangle U has sides of lengths 8, 5 and 5. What is the ratio of their areas?

Weekly Problem 16 - 2014

The diagrams show squares placed inside semicircles. What is the ratio of the shaded areas?

Weekly Problem 21 - 2014

A parallelogram is formed by joining together four equilateral triangles. What is the length of the longest diagonal?

Weekly Problem 49 - 2015

A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

Weekly Problem 33 - 2017

If the midpoints of the sides of a right angled triangle are joined, what is the perimeter of this new triangle?