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Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

DOTS Division

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}.

2-digit Square

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.