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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   Squaring special numbers (7 and
                 repeating 9's)

  1. Choose a number with a 7 and repeating 9's (use a mimimum of three 9's).
  2. The square is made up of:
    • first digits: 63 & two fewer 9's than repeating 9's in the number
    • next digits: 84 & one fewer 0 than repeating 9's in the number
    • last digit: 1

   Example:

  1. If the number to be squared is 7999:
  2. The square has:

    first digits: 63 and two fewer
        9's than rep. 9's            6 3 9
    next digits: 84 and one fewer
        0 than rep. 9's                   8 4 0 0
    last digit: 1                                 1

  3. So 7999 x 7999 = 63,984,001.

   See the pattern?

  1. If the number to be squared is 799999:
  2. The square has:

    first digits: 63 and two fewer
       9's than rep. 9's      6 3 9 9 9
    next digits: 84 and one fewer
       0 than rep. 9's                 8 4 0 0 0 0
    last digit: 1                                  1

  3. So 799999 x 799999 = 639,998,400,001.
     


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24 May 1999
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