Problem

Source: Cono Sur 2004 #1

Tags: number theory, cono sur



Maxi chose $3$ digits, and by writing down all possible permutations of these digits, he obtained $6$ distinct $3$-digit numbers. If exactly one of those numbers is a perfect square and exactly three of them are prime, find Maxi’s $3$ digits. Give all of the possibilities for the $3$ digits.