Which armies can be arranged in hollow square fighting formations?
In Napoleonic battles a hollow square was a popular formation for an infantry battalion designed to cope with Cavalry charges.
For example, the picture on the right shows a recreation of Wellington’s army at Waterloo.
Below are two diagrams showing symmetrical hollow square formations.
Charlie’s Method:
A general has 960 soldiers. How many different ways can he arrange his battalion in a symmetric hollow square?
What can you say about battalion sizes that can’t be arranged as symmetric hollow squares?
Can you find a general strategy for arranging any possible battalion into all possible symmetric hollow squares?
What about hollow squares that are not symmetric…?
You may also like to take a look at What’s Possible?
Age 14 to 16
