## Search found 188 matches

- Sat May 04, 2013 5:45 pm
- Forum: Secondary Level
- Topic: Circle circle
- Replies:
**1** - Views:
**1728**

### Re: Circle circle

Its a tedious work to illustrate the whole thing.Just the outline here. 1.Complete the equilateral triangle where the small circle is inscribed and find the length of sides of the triangle. 2.draw perpendiculars from the centers to the lines (lines that are mentioned in the que.) 3.Joint every verti...

- Sat May 04, 2013 4:47 pm
- Forum: Junior Level
- Topic: Brilliant problem
- Replies:
**1** - Views:
**1731**

### Brilliant problem

Any hint is expected..

*Consider the polynomial $P(x)=x^{3}+3x+1$ with roots $r_{1},r_{2},r_{3}$.

Find the value of $(r_{1}^{2}+r_{1}+1)(r_{2}^{2}+r_{2}+1)(r_{3}^{2}+r_{3}+1)$.

*Consider the polynomial $P(x)=x^{3}+3x+1$ with roots $r_{1},r_{2},r_{3}$.

Find the value of $(r_{1}^{2}+r_{1}+1)(r_{2}^{2}+r_{2}+1)(r_{3}^{2}+r_{3}+1)$.

- Fri May 03, 2013 10:14 pm
- Forum: Social Lounge
- Topic: Hello again
- Replies:
**0** - Views:
**2271**

### Hello again

After a long time,back again to flow with the tide of enthusiasm.My loving friends how are you?I missed the forum a lot during the absence.

- Thu Feb 28, 2013 10:01 pm
- Forum: Secondary Level
- Topic: Con..Con..confusion
- Replies:
**1** - Views:
**1743**

### Con..Con..confusion

I have a confusion in understanding a problem from Brilliant.org.Here is the problem and I request others not to give the solution nor the answer of the problem.I posted the problem to understand how the problem is operated! A sequence of polynomials $f_{k}(x)$ is defined as follows $f_{0}(x)=1$ ;$f...

- Wed Feb 27, 2013 1:59 pm
- Forum: Secondary Level
- Topic: Help with Combinatorics
- Replies:
**4** - Views:
**2489**

### Re: Help with Combinatorics

Look at the following examples,since you are reading Marcus I don't think you will have any problem understanding my languages. Consider the string:$AABBABA$,Now what you have to do is to make some words cutting from the main string.If you want to cut a $n$ digit word from the main string always cut...

- Fri Feb 22, 2013 4:02 pm
- Forum: Secondary Level
- Topic: Help me out!!!
- Replies:
**1** - Views:
**1380**

### Help me out!!!

Find the maximum value of the positive integer $n$ that satisfies the following inequality,

$a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+...+a_{n+1}^{2} \geq a_{n+1}(a_{1}+a_{2}+....+a_{n})$.

where $a_{i}$ is an arbitrary real number.$i \in (1,2,3,....,n+1)$.

$a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+...+a_{n+1}^{2} \geq a_{n+1}(a_{1}+a_{2}+....+a_{n})$.

where $a_{i}$ is an arbitrary real number.$i \in (1,2,3,....,n+1)$.

- Wed Feb 06, 2013 7:08 pm
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies:
**9** - Views:
**3662**

### Re: Rajshahi MO 2013, Secondary 1

And what is the answer for a regular n-gon where 'n' is even? I think that will be $\displaystyle \binom{n}{4}-\binom{\frac{n}{2}}{2}$ .

- Wed Feb 06, 2013 6:56 pm
- Forum: Secondary Level
- Topic: Number theoretic
- Replies:
**0** - Views:
**1059**

### Number theoretic

Prove that, $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}$ is never an integer for $n \geq 2$

- Thu Jan 31, 2013 5:20 pm
- Forum: Combinatorics
- Topic: Rubik's Cube Comb
- Replies:
**4** - Views:
**2722**

### Re: Rubik's Cube Comb

How?? :o :o Shouldn't it be $12! \times 2^{12} \times 8! \times 3^{8} ???$ I don't know If I am right or wrong...For the corner pieces the approach should be as below: "There are $8$ corner pieces,Each piece having $3$ colors.For our advantage,at first we assume that each corner piece is painted wit...

- Wed Jan 30, 2013 11:16 pm
- Forum: Social Lounge
- Topic: Tech.help
- Replies:
**0** - Views:
**1329**

### Tech.help

Can anyone reckon how to open the files in the CD we were given in Regional Olympiads?I can't open any of those files in my PC.Further,I searched for some appropriate software to open but Windows file association website shows the file type to be unknown.How can I fix the problem?