1. Choose a number with a 3 and repeating 6's.
2. The square is made up of:
   • first digits: 13 & two fewer 4's than repeating 6's
   • next digits: 39 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 3666:
2. The square has:

   first digits: 13 and two fewer
    4's than 6's                 1 3 4
next digits: 39 and one fewer
    5 than 6's                        3 9 5 5
last digit: 6                                 6

3. So 3666 × 3666 = 13,439,556.

   See the pattern?

1. If the number to be squared is 366666:
2. The square has:

   first digits: 13 and two fewer
   4's than 6's         1 3 4 4 4
next digits: 39 and one fewer
   5 than 6's                    3 9 5 5 5 5
last digit: 6                                6

3. So 366666 × 366666 = 134,443,955,556.