| [SOLVED] Combinatorics (2) | |
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Mohammad Descartes
Posts : 100 Join date : 2009-11-05 Age : 40 Location : Right behind you
| Subject: [SOLVED] Combinatorics (2) Sat Nov 07, 2009 7:24 pm | |
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Last edited by Mohammad on Mon Nov 16, 2009 10:06 pm; edited 1 time in total | |
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Bruno Admin
Posts : 184 Join date : 2009-09-15 Age : 36 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! | |
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Bruno Admin
Posts : 184 Join date : 2009-09-15 Age : 36 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! | |
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Mohammad Descartes
Posts : 100 Join date : 2009-11-05 Age : 40 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) | |
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Mohammad Descartes
Posts : 100 Join date : 2009-11-05 Age : 40 Location : Right behind you
| Subject: Re: [SOLVED] Combinatorics (2) Sat Nov 07, 2009 9:12 pm | |
| Now my normal heart rate is back | |
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Bruno Admin
Posts : 184 Join date : 2009-09-15 Age : 36 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! | |
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Mohammad Descartes
Posts : 100 Join date : 2009-11-05 Age : 40 Location : Right behind you
| Subject: sol Sun Nov 15, 2009 7:20 pm | |
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Bruno Admin
Posts : 184 Join date : 2009-09-15 Age : 36 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! | |
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| Subject: Re: [SOLVED] Combinatorics (2) | |
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| [SOLVED] Combinatorics (2) | |
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