BEATCALC:  Beat the Calculator!

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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 a 2-digit number by 891

  1. Select a 2-digit number.
  2. Multiply it by 9.
  3. If the product is 2 digits, subtract 1:
    X X _ _
    Then subtract the product from 100:
    _ _ X X
  4. If the product is 3 digits, add 1 to the first digit and
    subtract it from the product: X X X _ _
    Then subtract the last 2 digits of the product from 100: _ _ _ X X

   Example:

  1. The 2-digit number chosen to multiply by 891 is 11.
  2. Multiply by 9: 9 x 11 = 99
  3. Subtract 1: 99 - 1 = 98: 9 8 _ _
  4. Subtract the product from 100: 100 - 99 = 1:
    _ _ 0 1
  5. So 11 x 891 = 9,801.

   See the pattern?

  1. The 2-digit number chosen to multiply by 891 is 34.
  2. Multiply by 9: 9 x 34 = 270 + 36 = 306
  3. Add 1 to the first digit: 3 + 1 = 4
  4. Subtract 4 from the product: 306 - 4 = 302:
    3 0 2 _ _
  5. Subtract the last 2 digits from 100: 100 - 6 = 94:
    _ _ 9 4
  6. So 34 x 891 = 30,294.


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21 October 1996
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