Tutorial 92
Squaring special numbers (1 and repeating 6's)
  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 squared 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 squared 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.