1. Choose a a number made up of sixes.
2. The square is made up of:
   1. one fewer 4 than there are repeating 6's
   2. 3
   3. same number of 5's as 4's
   4. 6

   Example:

1. If the number to be squared is 666
2. The square of the number has:

    4's (one less than digits
     in number)           4 4
 3                             3
 5's (same number as 4's)        5 5
 6                                   6

3. So 666 × 3666333 = 443556.

   See the pattern?

1. If the number to be squared is 66666
2. The square of the number has:

    4's (one less than digits
      in number)           4 4 4 4
 3                                 3
 5's (same number as 4's)            5 5 5 5
 6                                           6

3. So 66666 × 66666 = 4444355556.