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BdMO Online Forum • Search

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Re: Initial order of first $n$ numbers

Hint:
There is a parity of every permutation: try to define it in useful terms.
by *Mahi*
Sun Aug 09, 2015 10:07 pm
 
Forum: Combinatorics
Topic: Initial order of first $n$ numbers
Replies: 1
Views: 352

Re: Rangpur Secondary 2011/3

Try to factorize $2048$ - it should be straightforward after the question.
by *Mahi*
Mon May 11, 2015 7:45 pm
 
Forum: Secondary: Solved
Topic: Rangpur Secondary 2011/3
Replies: 6
Views: 1533

Re: Bdmo 2013 secondary

Previously posted here http://www.matholympiad.org.bd/forum/vi ... =13&t=2928 , also pinned at the top of forum home page. Please, for common problems, search the forum at least once. Topic locked.
by *Mahi*
Tue Mar 03, 2015 12:36 am
 
Forum: Secondary Level
Topic: Bdmo 2013 secondary
Replies: 3
Views: 799

Re: USAMO 2009/5

Previously posted in IMO Marathon, you can see a few more solutions there -
viewtopic.php?p=13226#p13226
by *Mahi*
Thu Feb 26, 2015 7:34 pm
 
Forum: Geometry
Topic: USAMO 2009/5
Replies: 4
Views: 603

Re: Hello everyone

Hello Ahmen
I welcome you to BdMO Online Forum on behalf of everybody here!
I hope you'll find it enjoyable and enriching.
by *Mahi*
Thu Feb 26, 2015 7:16 pm
 
Forum: Introductions
Topic: Hello everyone
Replies: 1
Views: 764

Re: Vectors around Regular Polygon

\[\begin{align*} 2\sum_{i=1}^n \overrightarrow{OP_i} &= \sum_{i=1}^n (\overrightarrow{OP_i} + \overrightarrow{OP_{i+2}} )\\ &= k \sum_{i=1}^n \overrightarrow{OP_{i+1}} \end{align*}\] Where $k < 2$ as $\overrightarrow{OP_i} $ and $\overrightarrow{OP_{i+2}} $s are not in the same line. So, \[(...
by *Mahi*
Sun Feb 22, 2015 6:16 pm
 
Forum: Higher Secondary Level
Topic: Vectors around Regular Polygon
Replies: 4
Views: 774

Re: Binomial and power of 4(or 2?)

Typo? :?
$\binom{5}{2} \cdot 6 \cdot 11 = 660 < 4^5$
by *Mahi*
Thu Feb 19, 2015 1:09 pm
 
Forum: Algebra
Topic: Binomial and power of 4(or 2?)
Replies: 3
Views: 605

Re: power of 2 or binomial?

Or, you know, Cauchy–Schwarz -
\[(n+1)\binom{2n}n = (n+1)\left [ \binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 \right ] \]\[ \geq \left [ \binom{n}{0} + \binom{n}{1} + \cdots + \binom{n}{n} \right ]^2 = 4^n \]
by *Mahi*
Thu Feb 19, 2015 1:01 pm
 
Forum: Algebra
Topic: power of 2 or binomial?
Replies: 4
Views: 611

Re: parameters for cosine of angles in a triangle sum up to

Hint:

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$
by *Mahi*
Mon Feb 09, 2015 12:27 pm
 
Forum: Geometry
Topic: parameters for cosine of angles in a triangle sum up to 2
Replies: 2
Views: 505
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