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 (3 and
                 repeating 9's)

  1. Choose a number with a 3 and repeating 9's.
  2. The square is made up of:
    • first digits: 15 & one fewer 9 than repeating 9's
    • next digits: 2 & one fewer 0 than repeating 9's
    • last digit: 1

   Example:

  1. If the number to be squared is 3999:
  2. The square has:

    first digits: 15 and one fewer
        9 than 9's                     1 5 9 9
    next digits: 2 and one fewer
        0 than 9's                            2 0 0
    last digit: 1                                   1

  3. So 3999 x 3999 = 15,992,001.

   See the pattern?

  1. If the number to be squared is 399999:
  2. The square has:

    first digits: 15 and one fewer
       9 than 9's             1 5 9 9 9 9
    next digits: 2 and one fewer
       0 than 9's                        2 0 0 0 0
    last digit: 1                                  1

  3. So 399999 x 399999 = 159,999,200,001.
     


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6 September 1999
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