In a particular list of three-digit perfect squares, the first perfect square can be turned into each of the others by rearranging its digits. What is the largest number of distinct perfect squares that could be in the list

The Answer is Three.

That's the largest nmber of 3-digit perfect squares that could be on the list.

The list is so;

169 = 13²

196 = 14²

961 = 31²

The thre numbers, 1, 6, and 9 can be rearranged three ways to form three 3-digit perfect squares in 169, 196, and 961. No other arrangement of a 3-digit perfect square can yield more or equal.