How many tours visit each vertex of a cube once and only once? How
many return to the starting point?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
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?
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?
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
What is the longest stick that can be carried horizontally along a
narrow corridor and around a right-angled bend?