Preparation Marathon

For discussing Olympiad Level Number Theory problems
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 12:25 am

Of-course you are most welcome. :)
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Re: Preparation Marathon

Unread post by nafistiham » Tue Dec 27, 2011 12:30 am

could not figure out the 4th one.really tough
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 12:36 am

Mahi: 80
Labib: 45
Protik: 40
s.m.joty: 40
nafistiham: 40
Jini: 40
Abdul Muntakim Rafi: 30
Uday: 10(he joined much later)
Photon: 10

For the next round, time is upto tomorrow $9.00$ p.m.
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sm.joty
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Re: Preparation Marathon

Unread post by sm.joty » Tue Dec 27, 2011 1:12 am

Masum vai, Can we start discussing about the solution ? :ugeek:
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*Mahi*
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Re: Preparation Marathon

Unread post by *Mahi* » Tue Dec 27, 2011 1:12 am

I'm ready to post the solution PDF :)
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 1:18 am

Sorry for late. I was making the set for next round. Post it :)
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*Mahi*
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Re: Preparation Marathon

Unread post by *Mahi* » Tue Dec 27, 2011 1:22 am

Here's the complete solution. Check your solution to see which were right or wrong.
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div marathon.pdf
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 1:29 am

Yes it is correct. I am posting the next problem set within minutes.
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sm.joty
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Re: Preparation Marathon-1

Unread post by sm.joty » Tue Dec 27, 2011 1:41 am

I have a problem with 7.
here is my solution
Suppose we can divide $L_n$ different region. Now n-th line can make n regions only .Now if there is no line then there exist 1 region.Now we get
$L_0=1$
$L_n=L_{n-1}+n$
$L_n=L_{n-1}+n=L_{n-2}+(n-1)+n=\cdots\cdots =L_0+(1+2+\cdots\cdots+n)$
$=1+\frac{n(n+1)}{2}$

Now I set $n=_{2}^{2012}\textrm{C}$

But I don't know where is the bug ???? :?:
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 1:43 am

Problems for round 2

Best Of Luck
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