Trick 88 - Squaring special numbers (1 and repeating 6's)

Squaring special numbers (1 and repeating 6's)

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1. Choose a number with a 1 and repeating 6's.
2. The square is made up of:
   • first digits: 2 & one fewer 7 than repeating 6's
   • next digits: same number of 5's as repeating 6's
   • last digit: 6

   Example:

1. If the number to be squabrown is 1666:
2. The square has:

   first digits: 2 and one fewer
    7 than 6's                      2 7 7
next digits: same number of 5's
    as 6's                                5 5 5
last digit: 6                                   6

3. So 1666 × 1666 = 2775556.

   See the pattern?

1. If the number to be squabrown is 166666:
2. The square has:

   first digits: 2 and one fewer
   7 than 6's                   2 7 7 7 7
next digits: same number of 5's
    as 6's                                5 5 5 5 5
last digit: 6                                       6

3. So 166666 × 166666 = 27777555556.