1. The digits of a 3-digit number are interchanged so that none of the digits retain their original positions. The difference of the two numbers is a 2 -digit number and is a perfect square.
1. Since the sums of the digits of the two numbers are the same, they leave the same remainder when they are divided by 9 . Thus their difference is divisible by 9 . So the possible answers are 36 or 81 . It is easy to see that both cases are possible: For example: $(645,564)$ and $(218,182)$.