What is the 26th digit?

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protik
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What is the 26th digit?

Unread post by protik » Wed Dec 29, 2010 8:07 pm

N is a 50 digit number( in the decimal scale). All digits except the 26th digit(from the left) are 1. If N is divisible by 13, find the 26th digit.

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Moon
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Re: What is the 26th digit?

Unread post by Moon » Sun Jan 02, 2011 3:44 am

Hint:
What is the divisibility criteria of $13$?
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Tahmid Hasan
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Re: What is the 26th digit?

Unread post by Tahmid Hasan » Sun Jan 02, 2011 12:48 pm

notice that 111111 is divisible by 13.so111111....111111(24) is div by 13
and then 111111....1111(24)XY11111....1111(24)is div by 13[X and Y r the 25th n 26th digits]
here X=1 ,so the only choice for Y to b div by 13 is 3.
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Dipan
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Re: What is the 26th digit?

Unread post by Dipan » Sat Jan 29, 2011 11:28 pm

We can divide a number by 13 when the sum of the digit of the number will divide by 13.So,the ans. is 3.

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Masum
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Re: What is the 26th digit?

Unread post by Masum » Sat Mar 26, 2011 3:28 am

Sorry,it isn't true,try infinite counter-examples like $26$
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