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

   Example:

1. If the number to be squared is 3335:
2. The square has:

   three 1's (same as repeating 3's)  1 1 1
four 2's (one more than
   repeating 3's)                        2 2 2 2
a final 5                                        5

3. So the square of 3335 is 11,122,225.

   See the pattern?

1. If the number to be squared is 333335:
2. The square has:

   five 1's (same as
   repeating 3's)      1 1 1 1 1
six 2's (one more than
   repeating 3's)                2 2 2 2 2 2
a final 5                                     5

3. So the square of 333335 is 111,112,222,225.