1. Choose a number with a 2 and repeating 6's.
2. The square is made up of:
   • first digits: 7 & two fewer 1's than repeating 6's
   • next digits: 07 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 2666:
2. The square has:

   first digits: 7 and two fewer
    1's than 6's                   7 1
next digits: 07 and one fewer
    5 than 6's                        0 7 5 5
last digit: 6                                 6

3. So 2666 × 2666 = 7,107,556.

   See the pattern?

1. If the number to be squared is 266666:
2. The square has:

   first digits: 7 and two fewer
   1's than 6's             7 1 1 1
next digits: 07 and one fewer
   5 than 6's                      0 7 5 5 5 5
last digit: 6                                  6

3. So 266666 × 266666 = 71,110,755,556.