good problems

For discussing Olympiad Level Combinatorics problems
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the arrivals
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good problems

Unread post by the arrivals » Fri Jan 14, 2011 4:57 pm

it seems my last posted topic got much popularity :D :D
here some more similar and easy but tricky problems for the interest ones
1)In a race with 20horses,in how many places the 1st three places can be filled?? :shock:
2)If n points are placed on the circumference of a circle and all the lines connecting them are joined what is the largest number of point of intersection of these lines inside the circle that can be obtained?? :evil:
the arrivals
women of purity are for men of purity and hence men of purity are for women of purity - THE HOLY QURAN
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photon
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Re: good problems

Unread post by photon » Mon Feb 07, 2011 9:22 am

1st ans.
\[{20!\div (20-3)}=6840ways\]
Try not to become a man of success but rather to become a man of value.-Albert Einstein
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photon
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Re: good problems

Unread post by photon » Mon Feb 07, 2011 9:33 am

2nd prob.
A point can't intersect its 2 sides' points.
my ans . (n-2)!ways
Try not to become a man of success but rather to become a man of value.-Albert Einstein
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Cryptic.shohag
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Re: good problems

Unread post by Cryptic.shohag » Mon Feb 07, 2011 11:58 pm

photon wrote:2nd prob.
A point can't intersect its 2 sides' points.
my ans . (n-2)!ways
According to my solution, the answer should be nC4....
God does not care about our mathematical difficulties; He integrates empirically. ~Albert Einstein
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