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 [SOLVED] Combinatorics (2)

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Mohammad
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PostSubject: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 7:24 pm

Only two students could solve this problem Shocked the year I was taking part in this competition, included me, Embarassed
So are U ready for this challenge? 10$ as prize Basketball
Here is the problem uploading.com Combinatorics%2B2.PDF/


Last edited by Mohammad on Mon Nov 16, 2009 10:06 pm; edited 1 time in total
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Bruno
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PostSubject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 8:22 pm

Hello Mohammad!

Here is my solution! cheers
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Bruno
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PostSubject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 8:38 pm

P.S. Don't give me $10; instead, please buy me a pint of stout at Reggie's some time soon! drunken
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Mohammad
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PostSubject: Not even close!   Sat Nov 07, 2009 9:05 pm

Very nice wrong solution.
It is not an equivalence relation because (0,0,...,0) doesn't belong to any classes! Simply why (1,1,...,1) is in the vector space? if I take S=span {E_1,..,E_k} which E_k has one in i-th place but the rest of its entries are zero you will never get (1,1,..,1) Basketball
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Mohammad
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PostSubject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 9:12 pm

Now my normal heart rate is back Very Happy
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Bruno
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PostSubject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 9:15 pm

That's correct! I don't know what I was thinking. Indeed (1,1,...,1) need not be in k. It's a nice wrong proof though, as you say rabbit

I'll see what I can do!
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Mohammad
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PostSubject: sol   Sun Nov 15, 2009 7:20 pm

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PostSubject: Re: [SOLVED] Combinatorics (2)   Mon Nov 16, 2009 2:01 am

Beautiful! cheers Congrats for solving that during the competition.

It seems that problems which require a double-counting argument of some kind are popular in competitions. I knew it had to be one of those but I was never close to the answer. Your $10 was never in danger! flower
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