BdMO National Higher Secondary 2010/10

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

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)

User avatar
Moon
Site Admin
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Location: Dhaka, Bangladesh
Contact:

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.

sourav das
Posts: 461
Joined: Wed Dec 15, 2010 10:05 am
Location: Dhaka
Contact:

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......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

Post Reply