1. Choose a number with repeating 3's and a final 4.
2. The square is made up of:
   • the same number of 1's as there are digits in the number;
   • one fewer 5;
   • a final 6

   Example:

1. If the number to be squared is 3334:
2. The square has:

   four 1's (number of digits
   in number)             1 1 1 1
three 5's (one fewer)             5 5 5
a final 6                               6

3. So the square of 3334 is 11,115,556.

   See the pattern?

1. If the number to be squared is 333334:
2. The square has:

   six 1's          1 1 1 1 1 1
five 5's                     5 5 5 5 5
a final 6                              6

3. So the square of 333334 is 111,111,555,556.