Multiplying Three digit Numbers with Middle digit 3

1. Select a 3-digit number with a middle digit of 3 (last digit not zero).
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 third digits:
   _ _ _ _ X X.
4. The third digit from the right will be 2:
   _ _ 2 _ _.
5. The next digit to the left will be 7 times the first digit of the number plus 1 (keep carry):
   _ _ X _ _ _.
6. The first digits will be the square of the first digit plus the carry: 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 631, choose 639 as the second number (same first digits, third digits add to 10).
2. 1 × 9 = 09 (multiply the third digits) - last two digits:
   _ _ _ _ 0 9.
3. The third digit from the right is 2:
   _ _ 2 _ _ _.
4. 7 × 6 = 42, 42 + 1 = 43 (the next digit to the left is 7 times the first digit plus 1 (keep carry 4):
   _ _ 3 _ _ _ .
5. 6 × 6 = 36; 36 + 4 = 40 ( the first digits are the square of the first digit plus the carry:
   4 0 _ _ _ _.
6. >So 631 × 639 = 403209.