Weekly Problem 38 - 2011

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Weekly Problem 52 - 2011

Draw two intersecting rectangles on a sheet of paper. How many regions are enclosed? Can you find the largest number of regions possible?

Weekly Problem 27 - 2012

Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

Weekly Problem 39 - 2013

Which of the areas shown in the hexagons are equal to each other?

A 30cm x 40cm page of a book includes a 2cm margin on each side... What percentage of the page is occupied by the margins?

Weekly Problem 3 - 2009

What fraction of the area of this regular hexagon is the shaded triangle?

M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

Weekly Problem 25 - 2010

These four touching circles have another circle hiding amongst them...

Weekly Problem 49 - 2010

When I place a triangle over a small square, or cover a larger square with the same triangle, a certain proportion of each is covered. What is the area of the triangle?

Weekly Problem 7 - 2011

Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

Weekly Problem 33 - 2014

A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. What is the perimeter of the rectangle?

Weekly Problem 49 - 2014

A solid wooden cube is painted blue on the outside. The cube is then cut into 27 smaller cubes of equal size. What fraction of the total surface area of these new cubes is blue?

Weekly Problem 9 - 2015

How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

Weekly Problem 12 - 2015

Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?

Weekly Problem 15 - 2015

In the diagram, two lines have been draawn in a square. What is the ratio of the areas marked?

Weekly Problem 17 - 2015

A square contains two overlapping squares. What is the total of the shaded regions?

Weekly Problem 26 - 2015

What are the volume and surface area of this 'Cubo Vazado' or 'Emptied Cube'?

Weekly Problem 34 - 2015

Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

Weekly Problem 37 - 2015

A piece of card is folded to make an open box. Given its surface area, can you work out its volume?

Weekly Problem 38 - 2015

Where does the line through P that halves the figure shown meet the edge XY?

Weekly Problem 11 - 2016

Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

Weekly Problem 23 - 2016

The diagram shows a cuboid in which the area of the shaded face is one quarter of the area of each of the two visible unshaded faces. What is the area of one of the unshaded faces?

Weekly Problem 26 - 2016

A cube has each of its faces covered by one face of an identical cube, making a solid as shown. What is the surface area of the solid?

Weekly Problem 33 - 2016

In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

Weekly Problem 35 - 2016

What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

Weekly Problem 43 - 2016

In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

Weekly Problem 50 - 2016

A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?

Weekly Problem 20 - 2017

The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

Weekly Problem 17 - 2017

Yasmin has beds for peas and strawberries in her rectangular garden. She lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by 15m^2. What was the original area of her pea bed?

Weekly Problem 23 - 2017

Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

Weekly Problem 31 - 2017

The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

Weekly Problem 48 - 2017

What is the surface area of the solid shown?

Weekly Problem 52 - 2017

Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?