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Getting the maximum and the minimum with now

  1. Mar 9, 2009 #1
    In the following cryptarithmetic equation, each of the x’s represent a decimal digit, whether same or different, and “NOW” represents a three digit positive integer with no leading zero. Each of N, O and W represent a decimal digit, whether same or different.

    (N O W) * (N O W)
    = (x x x x x x N O W)/1983

    What are the respective minimum value and the maximum value of “NOW”?
     
    Last edited: Mar 9, 2009
  2. jcsd
  3. Mar 9, 2009 #2
    There are three values of NOW that satisfy the equation:
    272: 272 * 272 == 146710272 / 1983
    375: 375 * 375 == 278859375 / 1983
    647: 647 * 647 == 830101647 / 1983
    272 is the minimum and 647 is the maximum.
    This was found by brute force.
     
  4. Aug 11, 2009 #3
    Also found by Brute Force:
    There are three solutions:
    n=2 o=7 w=2 => now*now*1983=146710272
    n=3 o=7 w=5 => now*now*1983=278859375
    n=6 o=4 w=7 => now*now*1983=830101647

    Thus, the minimum value for now is 272 and the maximum is 647.
     
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