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The number N = 111...1 consists of 2006 ones. It is exactly divisible by 11. How many zeroes are
there in the quotient N/11

 Sep 12, 2020
 #1
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There are 506 zeros in N/11.

 Sep 12, 2020
 #2
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n=1010101010101010101010101010..........;s=0;p=0;cycle: s=(n%10);if(s==1,p=p+1, 0);n=(n div 10);if(n!=0, goto cycle,0);print"Total Num =",p

 

 

There are 2005 digits in the quotient of N/11.

 

1002 of them are zeros, and:

1003 of them are "1's"

 Sep 12, 2020

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