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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:
**868**

- Sun Aug 09, 2015 10:07 pm
- Forum: Combinatorics
- Topic: Initial order of first $n$ numbers
- Replies:
**1** - Views:
**727**

- Mon May 11, 2015 7:45 pm
- Forum: Secondary: Solved
- Topic: Rangpur Secondary 2011/3
- Replies:
**6** - Views:
**2352**

### 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:
**1321**

### 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:
**1102**

### 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:
**1** - Views:
**1198**

### 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:
**1434**

### 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:
**1091**

### 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:
**1147**

### 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:
**944**

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

Hint:

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$