Visualising and representing

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

Weekly Problem 19 - 2009
When I looked at the greengrocer's window I saw a sign. When I went in and looked from the other side, what did I see?

Use the diagram to investigate the classical Pythagorean means.

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Every third page number in this book has been omitted. Can you work out what number will be on the last page?

What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?