Squaring numbers made up of 3s

1. Choose a a number made up of threes.
2. The square is made up of:
   1. one fewer 1 than there are repeating 3's
   2. zero
   3. one fewer 8 than there are repeating 3's
      (same as the 1's in the square)
   4. nine.

Example:

1. If the number to be squared is 3333:
2. The square of the number has:
   three 1's (one fewer than
   digits in number) 1 1 1 _ _ _ _ _
   next digit is 0 _ _ _ 0 _ _ _ _
   three 8's (same number as 1's) _ _ _ _ 8 8 8 _
   a final 9 _ _ _ _ _ _ _ 9
3. So 3333 × 3333 = 11108889.