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http://matholympiad.org.bd/questions/bdmo-questions
Search found 1175 matches
- Sun Aug 09, 2015 10:22 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Problem Sets of Previous Years
- Replies: 1
- Views: 4728
- Sun Aug 09, 2015 10:07 pm
- Forum: Combinatorics
- Topic: Initial order of first $n$ numbers
- Replies: 1
- Views: 4856
- Mon May 11, 2015 7:45 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/3
- Replies: 6
- Views: 15208
Re: Rangpur Secondary 2011/3
Try to factorize $2048$ - it should be straightforward after the question.
- Tue Mar 03, 2015 12:36 am
- Forum: Secondary Level
- Topic: Bdmo 2013 secondary
- Replies: 3
- Views: 6370
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.
- Thu Feb 26, 2015 7:34 pm
- Forum: Geometry
- Topic: USAMO 2009/5
- Replies: 4
- Views: 6501
Re: USAMO 2009/5
Previously posted in IMO Marathon, you can see a few more solutions there -
viewtopic.php?p=13226#p13226
viewtopic.php?p=13226#p13226
- Thu Feb 26, 2015 7:16 pm
- Forum: Introductions
- Topic: Hello everyone
- Replies: 2
- Views: 16604
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.
I welcome you to BdMO Online Forum on behalf of everybody here!
I hope you'll find it enjoyable and enriching.
- Sun Feb 22, 2015 6:16 pm
- Forum: Higher Secondary Level
- Topic: Vectors around Regular Polygon
- Replies: 4
- Views: 13197
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, \[(2-k)\sum...
- Thu Feb 19, 2015 1:09 pm
- Forum: Algebra
- Topic: Binomial and power of 4(or 2?)
- Replies: 3
- Views: 6281
Re: Binomial and power of 4(or 2?)
Typo?
$\binom{5}{2} \cdot 6 \cdot 11 = 660 < 4^5$
$\binom{5}{2} \cdot 6 \cdot 11 = 660 < 4^5$
- Thu Feb 19, 2015 1:01 pm
- Forum: Algebra
- Topic: power of 2 or binomial?
- Replies: 4
- Views: 6785
Re: power of 2 or binomial?
Or, you know, Cauchy–Schwarz -
\[(n+1)\binom{2n}n = (n+1)\left [ \binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 \right ] \]\[ \geq \left [ \binom{n}{0} + \binom{n}{1} + \cdots + \binom{n}{n} \right ]^2 = 4^n \]
\[(n+1)\binom{2n}n = (n+1)\left [ \binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 \right ] \]\[ \geq \left [ \binom{n}{0} + \binom{n}{1} + \cdots + \binom{n}{n} \right ]^2 = 4^n \]
- 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: 5549
Re: parameters for cosine of angles in a triangle sum up to
Hint:
$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$
$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$