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N Nine Nuance (Posted on 2016-01-29) Difficulty: 3 of 5
Determine the minimum value of a positive integer N > 2 such that:
the number 199...991, containing precisely N nines, is divisible by 1991.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 3 of 6 |
    5   open "n9nuance.txt" for output as #2
   10   Midpart=90:Ct9=1
   20   Frontpart=100
   30   while Done=0
   40     N=Frontpart+Midpart+1
   50     if N @ 1991=0 then
   60        :if N>1991 then Done=1:print #2,N:endif
   70     if Done then print Ct9
   80     Frontpart=Frontpart*10
   90     Midpart=(Midpart+9)*10:Ct9=Ct9+1
  100   wend
  110   close #2


finds 182 9's.

The number N is definitely 184 digits long, with 182 9's:


1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991


  Posted by Charlie on 2016-01-29 10:47:03
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