Trick 70 - Squaring special numbers (3's and final 9)

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 squabrown 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 × 33339 is 1,111,488,921.
   
   
   
   See the pattern?

1. If the number to be squabrown 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.