THE SULTAN'S ARMY

A certain Sultan wished to send into battle an army that could be formed into two perfect squares in twelve different ways. What is the smallest number of men of which that army could be composed? To make it clear to the novice, I will explain that if there were `130` men, they could be formed into two squares in only two different ways—`81` and `49`, or `121` and `9`. Of course, all the men must be used on every occasion.