Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Can you describe this route to infinity? Where will the arrows take you next?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Weekly Problem 28 - 2007

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Weekly Problem 43 - 2007

The diagram shows 10 identical coins which fit exactly inside a wooden frame. What is the largest number of coins that may be removed so that each remaining coin is still unable to slide.

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 46 - 2007

When a solid cube is held up to the light, how many of the shapes shown could its shadow have?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

A collection of short Stage 3 and 4 problems on Visualising.

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?

Can you make a tetrahedron whose faces all have the same perimeter?

Weekly Problem 34 - 2015

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

Weekly Problem 9 - 2016

The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Weekly Problem 3 - 2012

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

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Explore the lattice and vector structure of this crystal.