Optimisation

problem
Wrapping gifts

Age

16 to 18

Challenge level

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?
problem
Maximum flow

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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?
problem
Cube net

Age

16 to 18

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 16

Challenge level

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

Age

11 to 18

Challenge level

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

Age

14 to 16

Challenge level

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