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)
BdMO National Higher Secondary 2010/10
Re: BdMO National Higher Secondary 2010/10
Related: viewtopic.php?f=13&t=33
"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.
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
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......($from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......($from$ "$THE$ $UGLY$ $TRUTH$" )