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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   Add a sequence from one to a selected
             1-digit number and back

  1. Choose a 1-digit number.
  2. Square it.

   Example:

  1. If the 1-digit number selected is 7:
  2. To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1
  3. Square 7: 49
  4. So the sum of all numbers from 1 through 7 and back is 49.

   See the pattern?

  1. If the 1-digit number selected is 9:
  2. To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
  3. Square 9: 81
  4. So the sum of all numbers from 1 through 9 and back is 81.

You will certainly be faster with your answer than someone adding all the numbers up on a calculator!
 


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11 October 1999
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