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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   Adding consecutive numbers between two
              numbers

   Choose two 2-digit numbers less than 20
     (no limits for experts).
   Add all the numbers between them:
  1. Add the numbers;
  2. Subtract the numbers and add 1;
  3. Multiply half the sum by this difference + 1, OR
    Multiply the sum by half the difference + 1.

   Example:

  1. If the two numbers selected are 6 and 19:
  2. Add the numbers: 6 + 19 = 25.
  3. Subtract the numbers: 19 - 6 = 13. Add 1: 13 + 1 = 14.
  4. Multiply 25 by half of 14: 25 x 7 = 175.
  5. So the sum of the numbers from 6 through 19 is 175.

   See the pattern?

  1. If the two numbers selected are 4 and 18:
  2. Add the numbers: 4 + 18 = 22.
  3. Subtract the numbers: 18 - 4 = 14. Add 1: 14 + 1 = 15.
  4. Multiply half of 22 by 15: 11 x 15 = 165 (10 x 15 + 15).
  5. So the sum of the numbers from 4 through 18 is 165.

Practice with examples restricted to less than 20, then advance to larger numbers. You will impress your friends when you beat the calculator.


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4 November 1996
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