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.
