BdMO National Higher Secondary 2010/10

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BdMO
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BdMO National Higher Secondary 2010/10

Unread post by BdMO » Mon Feb 07, 2011 12:11 am

Problem 10:
$a_1, a_2,\cdots , a_k, \cdots , a_n$ is a sequence of distinct positive real numbers such that $a_1 < a_2 < \cdots <a_k$ and $a_k > a_{k+1} > \cdots > a_n$. A Grasshopper is to jump along the real axis, starting at the point $O$ and making $n$ jumps to the right of lengths $a_1, a_2, \cdots , a_n$ respectively. Prove that, once he reaches the rightmost point, he can come back to point $O$ by making $n$ jumps to the left of lengths $a_1, a_2, \cdots , a_n$ in some order such that he never lands on a point which he already visited while jumping to the right. (The only exceptions are point $O$ and the rightmost point)

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Moon
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Re: BdMO National Higher Secondary 2010/10

Unread post by Moon » Mon Feb 07, 2011 12:17 am

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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Re: BdMO National Higher Secondary 2010/10

Unread post by sourav das » Tue Jan 29, 2013 4:55 pm

Please check the link for solution: viewtopic.php?f=13&t=33&p=13138#p13138
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

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