BDMO NATIONAL JUNIOR 2014/10

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Math Mad Muggle
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BDMO NATIONAL JUNIOR 2014/10

Unread post by Math Mad Muggle » Mon Jan 30, 2017 9:38 pm

please explain the solution which you are going to give
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Kazi_Zareer
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Re: BDMO NATIONAL JUNIOR 2014/10

Unread post by Kazi_Zareer » Mon Jan 30, 2017 10:42 pm

Hint:
Pigeonhole Principle
We cannot solve our problems with the same thinking we used when we create them.

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ahmedittihad
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Re: BDMO NATIONAL JUNIOR 2014/10

Unread post by ahmedittihad » Mon Jan 30, 2017 10:49 pm

Let $a_i$ be the number of chocolates eaten in total to day $i$. So, $0<a_1<a_2<...<a_{58}<101$ implies $15<a_1+15<a_2+15<...<a_{58}+15<116$. Now, among the $116$ numbers $a_1$,$...$, $a_{58}$, $a_1+15$,$...$, $a_{58}+15$. So there are indices $x$, $y$ such that $a_x+15=a_y$. Implying that Oindri ate exactly $15$ chocolates from day $x+1$ to day $y$.
Frankly, my dear, I don't give a damn.

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