What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

How many tours visit each vertex of a cube once and only once? How many return to the starting point?