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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   Dividing a repeating 6-digit number by 7, 11,
                13; subtract 101

  1. Select a 3-digit number.
  2. Repeat these digits to make a 6-digit number.
  3. Divide this 6-digit by 7, then 11, then 13.
  4. Subtract 101.
  5. The answer is the original number minus 101!

   Example:

  1. If the 3-digit number selected is 289:
  2. The 6-digit number is 289289.
  3. Divide by 7, then by 11, then by 13:
    the answer is 289.
  4. Subtract 101: 289 - 101 = 188
  5. So 289289 divided by 7, then 11, then 13 minus 101 is 188.

   See the pattern?

  1. If the 3-digit number selected is 983:
  2. The 6-digit number is 983983.
  3. Divide by 7, then by 11, then by 13:
    the answer is 983.
  4. Subtract 101: 983 - 101 = 882
  5. So 983983 divided by 7, then 11, then 13 minus 101 is 882.

Alter the last step to add or subtract other numbers and you will create many new exercises.


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23 December 1996
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