In Napoleonic battles a hollow square was a popular formation for an infantry battalion designed to cope with Cavalry charges.
The soldiers were arranged in a large square, with a square hole in the middle:
Try creating some hollow squares of your own and explore the number of soldiers needed.
Here are some questions you might like to consider:
- Can you find a hollow square formation for 80 soldiers? 120 soldiers? 200 soldiers?
- Can you find more than one hollow square formation for any of these?
- Are there any numbers of soldiers that can't be arranged in hollow square formation?
- Can you find a strategy to make every possible hollow square with a given number of soldiers?