Multiplying Three digit Numbers with Middle digit 1

1. Select a 3-digit number with a middle digit of 1.
2. Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
3. The last two digits will be the product of the first digits:
   _ _ _ 0 X or _ _ _ _ X X.
4. The third digit from the right will be 2:
   _ _ 2 _ _ or _ _ _ 2 _ _ .
5. The next digit to the left will be 3 times the first digit of the number (keep carry):
   _ X _ _ _ or _ _ X _ _ _.
6. The first digits will be the square of the first digit plus the carry:
   X _ _ _ _ or X X _ _ _ _.

As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.

Example:

1. If the first number is 814, choose 816 as the second number (same first digits, second digits add to 10).
2. 4 × 6 = 24 (multiply the first digits) - last two digits:
   _ _ _ _ 2 4.
3. The third digit from the right is 2: _ _ 2 _ _ .
   8 × 3 = 24 (the next digit to the left is 3 times the first digit (keep carry 2): _ _ 4 _ _ _ .
4. 8 × 8 = 64; 64 + 2 = 66 ( the first digits are the square of the first digit plus the carry:
   6 6 _ _ _ _.
5. So 814 × 816 = 664224.