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 (4 and
                 repeating 3's)

  1. Choose a number with a 4 and repeating 3's.
  2. The square is made up of:
    • first digits: 18 & one fewer 7 than repeating 3's
    • next digits: 4 & one fewer 8 than repeating 3's
    • last digit: 9

   Example:

  1. If the number to be squared is 4333:
  2. The square has:

    first digits: 18 and one fewer
        7 than 3's                   1 8 7 7
    next digits: 4 and one fewer
        8 than 3's                          4 8 8
    last digit: 9                                 9

  3. So 4333 x 4333 = 18,774,889.

   See the pattern?

  1. If the number to be squared is 433333:
  2. The square has:

    first digits: 18 and one fewer
       7 than 3's             1 8 7 7 7 7
    next digits: 4 and one fewer
       8 than 3's                        4 8 8 8 8
    last digit: 9                                  9

  3. So 433333 x 433333 = 187,777,488,889.
     


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5 October 1998
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