Visualising and representing

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

What shapes can be made by folding an A4 sheet of paper only once?

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?

A huge wheel is rolling past your window. What do you see?

A solid 'star' shape is created. How many faces does it have?

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

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?

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?