perplexus.info :: Just Math : How many 2010s?

How many 2010s? (Posted on 2014-09-17)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info