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There is a number formed by n copies of 2020 and 1 in the unit place. If this number is divisible by 11, what is the smallest possible value of n

 Jun 1, 2021
 #1
avatar+119780 
+2

I'm  not  exactly sure  what you  mean  by  n  copies, but I think it might be this...if  we  apply  alternating signs  to  each  digit  - generating a sum of the digits -  and  this  sum  is either  0  or  divisible by 11, then  the  number  is  divisible by 11

 

So

 

If  we  repeat   2020    8  times   and append    1  at  the end

 

We get

 

2020  2020  2020  2020  2020  2020   2020  2020 1

 

If we begin  with a plus sign on the first digit, all  the digits  will  be positive  and their sum =  33   which is divisible by 11

 

Note  :   202020202020202020202020202020201/11   =  18365472910927456382001836547291

 

So   n  =   8

 

 

cool cool cool

 Jun 1, 2021
 #2
avatar+368 
+2

i've done this one, u did it correct!

 Jun 1, 2021
 #3
avatar+119780 
0

OK....THX,   MWH    !!!!

 

(I wasn't too sure of my answer  ....  )

 

cool cool cool

CPhill  Jun 1, 2021

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