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[SOLVED] Combinatorics (2)

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Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 7:24 pm Only two students could solve this problem the year I was taking part in this competition, included me, So are U ready for this challenge? 10\$ as prize 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

Posts : 184
Join date : 2009-09-15
Age : 31
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 8:22 pm Hello Mohammad!Here is my solution!

Posts : 184
Join date : 2009-09-15
Age : 31
Location : the infinite, frictionless plane of uniform density

 Subject: 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!

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: 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)

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: Re: [SOLVED] Combinatorics (2)   Sat Nov 07, 2009 9:12 pm Now my normal heart rate is back

Posts : 184
Join date : 2009-09-15
Age : 31
Location : the infinite, frictionless plane of uniform density

 Subject: 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 I'll see what I can do!

Descartes

Posts : 100
Join date : 2009-11-05
Age : 35
Location : Right behind you

 Subject: sol   Sun Nov 15, 2009 7:20 pm

Posts : 184
Join date : 2009-09-15
Age : 31
Location : the infinite, frictionless plane of uniform density

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

 Subject: Re: [SOLVED] Combinatorics (2)

 [SOLVED] Combinatorics (2)
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