1. Choose a number with a 1 and repeating 3's.
2. The square is made up of:
   • first digits: 1 & one fewer 7 than repeating 3's
   • next digits: 6 & one fewer 8 than repeating 3's
   • last digit: 9

   Example:

1. If the number to be squared is 1333:
2. The square has:

   first digits: 1 and one fewer
    7 than 3's                      1 7 7
next digits: 6 and one fewer
    8 than 3's                            6 8 8
last digit: 9                                   9

3. So 1333 × 1333 = 1776889.

   See the pattern?

1. If the number to be squared is 133333:
2. The square has:

   first digits: 1 and one fewer
   7 than 3's               1 7 7 7 7
next digits: 6 and one fewer
   8 than 3's                        6 8 8 8 8
last digit: 9                                  9

3. So 133333 × 133333 = 17777688889.