Squaring a repeating 6-digit number

1. Choose a number with repeating 6's .
2. The square is made up of:
   • One less 4 than there are digits in the number;
   • One 3;
   • The same number of 5's as 4's;
   • A final 6.

   Example:

1. If the number to be squared is 666:
2. The square has:

   one less 4 than digits in
   the number                 4 4
one 3                             3
same number of 5's as 4's           5 5
a final 6                               6

3. So the square of 666 is 443556.

   See the pattern?

1. If the number to be squared is 66666:
2. The square has:

   one less 4 than digits in
   the number)                 4 4 4 4
one 3                                  3
same number of 5's as 4's                5 5 5 5
a final 6                                        6

3. So the square of 66666 is 4444355556.