1. Choose a number with repeating 3's and a final 1.
2. The square is made up of:
   • One fewer 1 than there are repeating 3's
   • 09
   • The same number of 5's as there are 1's in the square;
   • A final 61

   Example:

1. If the number to be squared is 3331:
2. The square has:

   Two 1's (one fewer than
   repeating 3's)           1 1
Next digits: 09                 0 9
Two 5's (same as 1's in square)     5 5
A final 61                              6 1

3. So the square of 3331 is 11,095,561.

   See the pattern?

1. If the number to be squared is 333331:
2. The square has:

   Four 1's (one fewer than
   repeating 3's)       1 1 1 1
Next digits: 09                 0 9
Four 5's (same as 1's in square)    5 5 5 5
A final 61                                  6 1

3. So the square of 333331 is 111,109,555,561.