Weekly Problem 36 - 2011

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Weekly Problem 37 - 2011

Rotating a pencil twice about two different points gives surprising results...

Weekly Problem 39 - 2011

Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radius.

Weekly Problem 4 - 2012

What fraction of the volume of this can is filled with lemonade?

Weekly Problem 4 - 2006

Work out the radius of a roll of adhesive tape.

Weekly Problem 5 - 2006

How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

Weekly Problem 7 - 2006

It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?

Weekly Problem 13 - 2006

If three runners run at the same constant speed around the race tracks, in which order do they finish?

Weekly Problem 19 - 2006

What is the total area enclosed by the three semicicles?

Weekly Problem 42 - 2006

Can you work out the shaded area surrounded by these arcs?

Weekly Problem 11 - 2007

A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

Weekly Problem 15 - 2008

Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

Weekly Problem 24 - 2008

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?

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 34 - 2010

Can you work out the fraction of the larger square that is covered by the shaded area?

Weekly Problem 51 - 2010

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Weekly Problem 30 - 2011

Three touching circles have an interesting area between them...

Weekly Problem 49 - 2006

What is the area of the shape enclosed by the line and arcs?

Weekly Problem 7 - 2014

The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?

Weekly Problem 23 - 2014

Boris' bicycle has a bigger back wheel than front wheel. Can you work out how many revolutions the back wheel made if the front wheel did 120,000?

Weekly Problem 29 - 2014

snail is at one corner of a cube. What proportion of the surface of the cube could the snail reach in one hour?

Weekly Problem 52 - 2014

Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

Weekly Problem 5 - 2015

The diagram shows four equal discs and a square. What is the perimeter of the figure?