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 (9's and final 5)

  1. Choose a number with repeating 9's and a final 5.
  2. The square is made up of:
    • same number of 9's as there are repeating 9's
    • same number of 0's
    • a final 25

   Example:

  1. If the number to be squared is 9995:
  2. The square has:

    same number of 9's as
       repeating 9's:         9 9 9
    same number of 0's as 9's
       in the square               0 0 0
    a final 25                           2 5

  3. So 9995 x 9995 = 99900025.

   See the pattern?

  1. If the number to be squared is 999995:
  2. The square has:

    same number of 9's as
       repeating 9's:        9 9 9 9
    same number of 0's as 9's
       in the square                0 0 0 0
    a final 25                              2 5

  3. So 999995 x 999995 = 999990000025.


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20 April 1998
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