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.

   See the pattern?

1. If the number to be squared is 333:
2. The square of the number has:

   two 1's                          1 1 _ _ _ _ _
next digit is 0                  _ _ _ 0 _ _ _
two 8's                          _ _ _ _ 8 8 _
a final 9                        _ _ _ _ _ _ 9

3. So 333 × 333 = 110889.