Squaring numbers between 4000 and 4099

1. Choose a number between 4000 and 4099.
2. For numbers less than 4013:
3. The first three digits are: 1 6 0 _ _ _ _ _
4. The next two digits are 8 times the last two digits:
   _ _ _ X X _ _ _
5. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
   _ _ _ _ _ X X X

   Example:

1. If the number to be squared is 4005:
2. The first three digits are: 1 6 0 _ _ _ _ _
3. The next two digits are 8 times the last two:
   8 x 5 = 40: _ _ 4 0 _ _ _
4. For the last three digits, square the last two:
   5 x 5 = 25: _ _ _ _ _ 0 2 5
5. So 4005 x 4005 = 16,040,025.

   See the pattern?

For numbers greater than 4012, reverse the order:
1. If the number to be squared is 4080:
2. For the last three digits, square the last two:
   80 x 80 = 6400, carry 6: _ _ _ _ 4 0 0
3. The middle two digits are 8 times the last two (keep the carry):
   8 x 80 = 640 (keep carry of 6), 40 + 6:
   _ _ _ 4 6 _ _ _
4. The first three digits are 160 + the carry:
   160 + 6 = 166: 1 6 6 _ _ _ _ _
5. So 4080 x 4080 = 16,646,400.