Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?

Hollow Squares

Age 14 to 16 Challenge Level

You may want to start by exploring how many hollow square arrangements there are for smaller battalions.

Perhaps look for hollow square arrangements of 48, 80, and 120 people.