Optimisation

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

What's the largest volume of box you can make from a square of paper?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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?

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.

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