1. Choose a number with a 9 and repeating 6's (use at least three 6's).
2. The square is made up of:
   • first digits: 93 & two fewer 4's than repeating 6's
   • next digits: 31 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 9666:
2. The square has:

   first digits: 93 and two fewer
    4's than 6's                9 3 4
next digits: 31 and one fewer
    5 than 6's                        3 1 5 5
last digit: 6                                 6

3. So 9666 × 9666 = 93,431,556.

   See the pattern?

1. If the number to be squared is 966666:
2. The square has:

   first digits: 93 and two fewer
   4's than 6's           9 3 4 4 4
next digits: 31 and one fewer
   5 than 6's                      3 1 5 5 5 5
last digit: 6                                  6

3. So 966666 × 966666 = 934,443,155,556.