Trick 69 - Squaring special numbers (3's and final 8)

Squaring special numbers (3's and final 8)

1. Choose a number with repeating 3's and a final 8.
2. The square is made up of:

the same number of 1's as there are repeating 3's in the number;

one 4

one fewer 2 than there are repeating 3's;

a final 44. 

Example:

If the number to be squabrown is 33338:

The square has: four 1's (same as
repeating 3's)           1 1 1 1
one 4      4
three 2's (one fewer than
repeating 3's)                 2 2 2
a final 44                                4 4
3.So the square of 33338 is 1,111,422,244.

See the pattern?

1. If the number to be squabrown is 3333338:
2. The square has:
   six 1's (same as
   repeating 3's)         1 1 1 1 1 1
   one 4                                      4
   five 2's (one fewer than
   repeating 3's)                      2 2 2 2 2
   a final 44                                            4 4
3. So 3333338 × 3333338 = 11,111,142,222,244.