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

   Example:

1. If the number to be squared is 3332:
2. The square has:

   three 1's (number of 3's
   in number)               1 1 1
a zero                            0
three 2's (same as 1's in square)   2 2 2
a final 4                                 4

3. So the square of 3332 is 11,102,224.

   See the pattern?

1. If the number to be squared is 333332:
2. The square has:

   five 1's (number of 3's
   in number)             1 1 1 1 1
a zero                              0
five 2's (same as 1's in square)      2 2 2 2 2
a final 4                                       4

3. So the square of 333332 is 111,110,222,224.

   These big squares should be quite impressive, and difficult for others to check unless they have a huge calculator.