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 297

  1. Select a 2-digit number.
  2. Multiply by 3.
  3. If the product has 2 digits, subtract 1:
    X X _ _
    Subtract the product from 100: _ _ X X
  4. If the product has 3 digits, add 1 to the first digit:
    X X X _ _
    Subtract this from the product;
    Subtract the last 2 digits of the product from 100:
    _ _ _ X X

   Example:

  1. The 2-digit number chosen to multiply by 297 is 33.
  2. Multiply by 3: 3 x 33 = 99.
  3. Subtract 1: 99 - 1 = 98: 9 8 _ _
  4. 100 - product: 100 - 99 = 1: _ _ 0 1
  5. So 297 x 33 = 9801.

   See the pattern?

  1. The 2-digit number chosen to multiply by 297 is 92.
  2. Multiply by 3: 3 x 92 = 276.
  3. Add 1 to the first digit: 2 + 1 = 3
  4. Subtract this from the product: 276-3 = 273:
    2 7 3 _ _
  5. Subtract the last two digits of the product from 100:
    100 - 76 = 24: _ _ _ 2 4
  6. So 297 x 92 = 27324..


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9 June 1997
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