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 495

  1. Select a 2-digit number .
  2. Multiply by 5.
  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 _ _ (don't add 1 if the last two digits are zeros)
    Subtract this from the product: X X X _ _
    Subtract the last 2 digits of the product from 100:
    _ _ _ X X

   Example:

  1. The 2-digit number chosen to multiply by 495 is 18.
  2. Multiply by 5: 5 x 18 = 90.
  3. Subtract 1: 90 - 1 = 89: 8 9 _ _
  4. 100 - product: 100 - 90 = 10: _ _ 1 0
  5. So 495 x 18 = 8910.

   See the pattern?

  1. The 2-digit number chosen to multiply by 495 is 67.
  2. Multiply by 5: 5 x 67 = 300 + 35 = 335.
  3. Add 1 to the first digit: 3 + 1 = 4
  4. Subtract this from the product: 335-4 = 331:
    3 3 1 _ _
  5. Subtract the last two digits of the product from 100:
    100 - 35 = 65: _ _ _ 6 5
  6. So 495 x 67 = 33165.


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7 July 1997
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