Starter of the Week 15: Hollow Squares
A hollow square was a battle formation used in the 1800s. This consisted of a hollow square inside a larger square where the generals could safely command their troops.
Here we can see that 12 men can be arranged in a hollow square formation (12 = 4 squared – 2 squared).
How many other numbers of men between 10 and 20 can be arranged in hollow squares?
Can you make a hypothesis about which numbers of men can’t be arranged in hollow squares?
Can you prove your hypothesis?
Level of difficulty: The first part accessible for all students, the proof part accessible to Analysis students.
Syllabus knowledge required: None – but would fit well with ideas of proof or as an example of a more proof based IA (possibly combined with computing). The last part requires some knowledge about ideas of proof.
You can donwnload the solution here