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How many 2010s? (Posted on 2014-09-17) Difficulty: 1 of 5
If 20102010...2010729 (the number 2010 is repeated precisely n times followed by 729) is divisible by 11, find the least possible value of n.

No Solution Yet Submitted by K Sengupta    
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Solution solution Comment 1 of 1
answer : 10

Consider the number 20102010...2010729, where  2010 is repeated n times.
The sum of digits on odd- counting from left- places is  3n+16
Ob even the sum is 2

COMPARING MODULO 11:
3n+16=3n+5=2 mod11

3n=8 mod 11
3*10=30  22+8
Since 10 is less than 11 , it is a minimal soluition
-

21,32,43 etc would work as well


  Posted by Ady TZIDON on 2014-09-17 08:05:16
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