Reasoning, convincing and proving

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?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Here are shadows of some 3D shapes. What shapes could have made them?

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?