Preparation Marathon

For discussing Olympiad Level Number Theory problems
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*Mahi*
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Re: Preparation Marathon-1

Unread post by *Mahi* » Tue Dec 27, 2011 1:49 am

sm.joty wrote:I have a problem with 7.
here is my solution
Now n-th line can make n regions only .
It varies. n-th line can create from 1 to $\frac {\sqrt {8n+1}-1}{2}$ regions.
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Masum
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Re: Preparation Marathon-1

Unread post by Masum » Tue Dec 27, 2011 1:51 am

sm.joty wrote: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 ???? :?:
You have counted the number of different regions with $n$ lines, not the given $\binom n2$ lines I think and then you set $\binom n2$
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Masum
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Re: Preparation Marathon

Unread post by Masum » Tue Dec 27, 2011 1:55 am

Final scores:(inform me if someone is missing)
viewtopic.php?f=26&t=1487&p=7446#p7446
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sm.joty
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Re: Preparation Marathon

Unread post by sm.joty » Tue Dec 27, 2011 2:04 am

@Mahi I tried to say, n-th line can make maximum n regions.

@Masum vai, I check this formula for n=2,3. And I try to establish the general form and then set a value for n.
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Shihab
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Re: Preparation Marathon

Unread post by Shihab » Tue Dec 27, 2011 8:52 am

I'v just registered in this forum. When I'm trying to send a PM it shows:
"We are sorry, but you are not authorised to use this feature. You may have just registered here and may need to participate more to be able to use this feature."

What should I do?

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sm.joty
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Re: Preparation Marathon

Unread post by sm.joty » Tue Dec 27, 2011 1:09 pm

@Shihab, I think Moon vai, or other global moderators can do something. But I guess if you attend with us by posting your opinion in any topic, then you can use this feature. Because number of your posts is very poor. So you can visit the other sections and keep discussing with others.
And for this Preparation Marathon I think, Masum vai can do something for you. :)

@Masum vai, In Preparation Marathon-2, 3 no. question says that there can 1 member in a team. Can I say that the only person is the Captain. I'm being confused about the condition of captain ?? :?:

In 10 no. it's quite hard to find out the next term. because there is only 4 terms......


@Mahi, I can't understand your 7 no. solution. Could you explain please ??
and for which condition I can say, $26^p+1$ is divisible by $27$ ?
হার জিত চিরদিন থাকবেই
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Labib
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Re: Preparation Marathon

Unread post by Labib » Tue Dec 27, 2011 1:33 pm

@Jyoti, $26\equiv -1 (mod 27)$
@ Masum vai,
Masum wrote: $8.$ There are $10$ horizontal lines and $8$ vertical lines. Connect all the points.
How many intersections are there?$
Which points are we talking about, here??
I mean, are these the points of intersection of the lines?? (lines don't have ends, so they should be the only ones I think... :?)
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zadid xcalibured
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Re: Preparation Marathon

Unread post by zadid xcalibured » Tue Dec 27, 2011 1:51 pm

certainly there is a problem in your problem.if all the rectangles are similar then the number of intrsctn will be less than the nmbr of intrsctn when they are not similar.

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zadid xcalibured
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Re: Preparation Marathon

Unread post by zadid xcalibured » Tue Dec 27, 2011 2:02 pm

@labib.u will get some intrsctn points by the hrzntl lines and vrtcl lines.connect these points with every other points.then ull get some lines.determine the numbers of their intrsctns.

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Abdul Muntakim Rafi
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Re: Preparation Marathon

Unread post by Abdul Muntakim Rafi » Tue Dec 27, 2011 2:12 pm

১।মানি না। আমি আগের টার ৩ টা সল্ভ করছি। আজকে আরও কয়েকটা করব মনে করছিলাম। কিন্তু আগেরটার উত্তর দিয়ে দেওয়া হইছে। :(

২।আর আমার মনে হয় এক দিনের পরিবর্তে দুই দিন সময় দেওয়া উচিত।

৩।আর প্রশ্ন সহজ থেকে কঠিন এভাবে সাজানো উচিত। National এর মত। :idea:

PS: Don't mind about all these advices... Just giving my opinion as a member... But if most of the members agree Masum bhai please think about "আর আমার মনে হয় এক দিনের পরিবর্তে দুই দিন সময় দেওয়া উচিত।"
Man himself is the master of his fate...

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