BEATCALC:  Beat the Calculator!

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Back to Calculation Tips & Tricks
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From the BEATCALC mailing list:
a weekly service from B. Lee Clay, archived here by the Math Forum.
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   Multiplying two selected 3-digit numbers
            (middle digit 0)

  1. Select a 3-digit number with a middle digit of 0.
  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 first digit(s) will be the square of the first digit:
    X _ _ _ _ or X X _ _ _ _.
  4. The next digit will be the first digit of the numbers:
    _ X _ _ _ or _ _ X _ _ _.
  5. The next digit is zero: _ _ 0 _ _ or _ _ _ 0 _ _.
  6. The last two digits will be the product of the third digits:
    _ _ _ X X or _ _ _ _ X X.

   Example:

  1. If the first number is 407, choose 403 as the second number (same first digits, second digits add to 10).
  2. 4 x 4 = 16 (square the first digit): 1 6 _ _ _ _.
  3. The next digit will be the first digit of the numbers:
    _ _ 4 _ _ .
  4. The next digit is zero: _ _ 0 _ _ .
  5. 7 x 3 = 21 (the last two digits will be the product of the third digits: _ _ _ 2 1.
  6. So 407 x 403 = 164021.

   See the pattern?

  1. If the first number is 201, choose 209 as the second number (same first digits, second digits add to 10).
  2. 2 x 2 = 4 (square the first digit): 4 _ _ _ _.
  3. The next digit will be the first digit of the numbers:
    _ 2 _ _ _ .
  4. The next digit is zero: _ _ 0 _ _ .
  5. 1 x 9 = 09 (the last two digits will be the product of the third digits: _ _ _ 0 9.
  6. So 201 x 209 = 42009.


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14 January 1996
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