Trick 116 - Multiplying two selected 3-digit numbers (middle digit 2)

Multiplying two selected 3-digit numbers (middle digit 2)

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1. Select a 3-digit number with a middle digit of 2.
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 6: _ _ 6 _ _.
5. The next digit to the left will be 5 times the first digit of the number (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 622, choose 628 as the second number (same first digits, third digits add to 10).
2. 2 × 8 = 16 (multiply the third digits) - last two digits:
   _ _ _ _ 1 6.
3. The third digit from the right is 6: _ _ 6 _ _ _.
4. 5 × 6 = 30 (the next digit to the left is 5 times the first digit (keep carry 3): _ _ 0 _ _ _ .
5. 6 × 6 = 36; 64 + 3 = 39 ( the first digits are the square of the first digit plus the carry: 3 9 _ _ _ _.
6. So 622 × 628 = 390616.

   See the pattern?

1. If the first number is 221, choose 229 as the second number (same first digits, third digits add to 10).
2. 1 × 9 = 9 (multiply the third digits) - last two digits:
   _ _ _ 0 9.
3. The third digit from the right is 6: _ _ 6 _ _.
4. 5 × 2 = 10 (the next digit to the left is 5 times the first digit (keep carry 1): _ 0 _ _ _ .
5. 2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus the carry: 5 _ _ _ _.
6. So 221 × 229 = 50609.