1. Choose a number with a 5 and repeating 6's.
2. The square is made up of:
   • first digits: 32 & two fewer 1's than repeating 6's
   • next digits: 03 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 5666:
2. The square has:

   first digits: 32 and two fewer
    1's than 6's                 3 2 1
next digits: 03 and one fewer
    5 than 6's                        0 3 5 5
last digit: 6                                 6

3. So 5666 × 5666 = 32,103,556.

   See the pattern?

1. If the number to be squared is 566666:
2. The square has:

   first digits: 32 and two fewer
   1's than 6's           3 2 1 1 1
next digits: 03 and one fewer
   1 than 6's                      0 3 5 5 5 5
last digit: 6                                  6

3. So 566666 × 566666 = 321,110,355,556.