Squaring special numbers (3's and final 9)

1. Choose a number with repeating 3's and a final 9.
2. The square is made up of:
   • the same number of 1's as there are repeating 3's in the number;
   • one 4
   • two fewer 8's than there are repeating 3's;
   • a final 921.

   Example:

1. If the number to be squared is 33339:
2. The square has:

   four 1's (same as
   repeating 3's)     1 1 1 1
one 4                         4
two 8's (two fewer than
   repeating 3's)               8 8
a final 921                         9 2 1

3. So 33339 x 33339 is 1,111,488,921.

   See the pattern?

1. If the number to be squared is 3333339:
2. The square has:

   six 1's (same as
   repeating 3's)   1 1 1 1 1 1
one 4                           4
four 8's (two fewer than
   repeating 3's)                 8 8 8 8
a final 921                               9 2 1

3. So the square of 3333339 = 11,111,148,888,921.