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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 Answer only | Comment 1 of 6

N=180   Aided by Excel only.

edited : I have erroneously started with  N(0)=1991,

and continued : h(K)=mod(N(K),1991)

N(K)= MOD(10*h(K-1)+81),1991

So the value 0 is reached when  N=182 (corrected answer).

Edited on January 29, 2016, 3:44 pm
  Posted by Ady TZIDON on 2016-01-29 09:24:59

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