2D representations of 3D shapes

problem
The spider and the fly

Age

14 to 16

Challenge level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
problem
Moving squares

Age

14 to 16

Challenge level

How can you represent the curvature of a cylinder on a flat piece of paper?
problem
Perfect eclipse

Age

14 to 16

Challenge level

Use trigonometry to determine whether solar eclipses on earth can be perfect.
problem
Stadium sightline

Age

14 to 18

Challenge level

How would you design the tiering of seats in a stadium so that all spectators have a good view?
problem
Torus patterns

Age

16 to 18

Challenge level

How many different colours would be needed to colour these different patterns on a torus?