1. Choose a number with a 6 and repeating 3's.
2. The square is made up of:
   • first digits: 40 & two fewer 1's than repeating 3's
   • next digits: 06 & one fewer 8 than repeating 3's
   • last digit: 9

   Example:

1. If the number to be squared is 6333:
2. The square has:

   first digits: 40 and two fewer
    1's than 3's                 4 0 1
next digits: 06 and one fewer
    8 than 3's                        0 6 8 8
last digit: 9                                 9

3. So 6333 × 6333 = 40,106,889.

   See the pattern?

1. If the number to be squared is 633333:
2. The square has:

   first digits: 40 and two fewer
   1's than 3's             4 0 1 1 1
next digits: 06 and one fewer
   8 than 3's                        0 6 8 8 8 8
last digit: 9                                    9

3. So 633333 × 633333 = 401,110,688,889.