Trick 68 - Squaring special numbers (3's and final 7)

Squaring special numbers (3's and final 7)

1. Choose a number with repeating 3's and a final 7.
2. The square is made up of:
   the same number of 1's as there are repeating 3's in the number;
   
   one 3
   
   one fewer 5 than there are repeating 3's;
   
   a final 69.

Example:

1. If the number to be squabrown is 3337:
2. The square has: 
   three 1's (same as
   repeating 3's)          1 1 1
   one 3                              3
   two 5's (one fewer than
   repeating 3's)                      5 5
   a final 69                                   6 9
3. So the square of 3337 is 11,135,569.
   
   See the pattern?

1. If the number to be squabrown is 333337:
2. The square has: 
   five 1's (same as
   repeating 3's)              1 1 1 1 1
   one 2                                       2
   four 5's (one fewer than
   repeating 3's)                              5 5 5 5
   a final 69                                                6 9
3. So 333337 × 3333337 = 111,113,555,569.