## Search found 73 matches

- Tue Feb 13, 2018 10:34 pm
- Forum: Junior Level
- Topic: Need a solution to my question please.
- Replies:
**1** - Views:
**3869**

### Re: Need a solution to my question please.

We need to take minimum amount of kittens. Firstly, we will take the rightest kitten of the first box. So, the rest $7$ kittens, on the left, will simply run away. In the $2^{nd}$ box, let the leftest kitten has been taken. So, $7$ kittens at right will go to the $3^{rd}$ box. In the $3^{rd}$ box, t...

- Tue Feb 13, 2018 8:47 pm
- Forum: Secondary Level
- Topic: secondary regional 2017
- Replies:
**2** - Views:
**3424**

### Re: secondary regional 2017

$\frac{AE}{EC} \times \frac{DC}{DB} \times \frac{BF}{AF}= \frac{1}{3} \frac{2}{1} \frac{3}{2}=1$ So, check

**Ceva's Theorem**- Tue Feb 13, 2018 8:33 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2017 National Round Secondary 7
- Replies:
**14** - Views:
**5470**

### Re: BdMO 2017 National Round Secondary 7

$K$ may not be $2$

- Tue Feb 13, 2018 8:27 pm
- Forum: Site Support
- Topic: Regional Olympiad 2016
- Replies:
**3** - Views:
**12210**

### Re: Regional Olympiad 2016

In $\triangle ABC,\angle BAC=50^\circ,\angle ACB=65^\circ$. So, $\angle ABC=180^\circ-50^\circ-65^\circ=65^\circ$ So, $\angle ABC=\angle ACB \Rightarrow AB=AC$ So, $AB=AC=AD$ Between $\triangle ABF$ and $\triangle ADF, AB=AD,AF=AF,\angle AFB=\angle AFD=90^\circ$ So, $\triangle ABF \cong \triangle AD...

- Tue Feb 13, 2018 7:47 pm
- Forum: Secondary Level
- Topic: Triangle geometry
- Replies:
**5** - Views:
**4622**

### Re: Triangle geometry

Do you want to mean

Then, they intersect at a single point, no triangle comes out.

**"Joining $AD,BE,CF$"**?Then, they intersect at a single point, no triangle comes out.

**[If I don't miss anything]**- Sat Feb 10, 2018 11:55 pm
- Forum: Secondary Level
- Topic: Find Formula for Sequence
- Replies:
**2** - Views:
**1298**

### Re: Find Formula for Sequence

Actually I wanted full solution! :idea: $a_n=2a_{n-1}+2a_{n-2} \Rightarrow r^2=2r+1 \Rightarrow r^2-2r-1=0$ $r= \frac{-(-2)+ \sqrt {(-2)^2-4.1.(-1)}}{2.1}$ or,$\frac{-(-2)- \sqrt {(-2)^2-4.1.(-1)}}{2.1}$ $\Rightarrow r=(1+i)$ or, $(1-i)$ Let $\alpha =(1+\sqrt 2)$ and, $\beta =(1-\sqrt 2)$ We can sa...

- Sat Feb 10, 2018 11:28 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2017 National Round Secondary 8
- Replies:
**2** - Views:
**1997**

### Re: BdMO 2017 National Round Secondary 8

I think the first step has come through it: We can right:$a_{n+1}=2a_n-2a_{n-1} \Rightarrow a_n=2a_{n-1}-2a_{n-2} \Rightarrow r^2=2r-2 \Rightarrow r^2-2r+2=0$ $r=\frac{-(-2)+\sqrt{(-2)^2-4.1.2}}{2.1}$ or,$\frac{-(-2)-\sqrt{(-2)^2-4.1.2}}{2.1}$ $\Rightarrow r=(1+i) or, (1-i)$ [Because $\sqrt{(-2)^2-...

- Sat Feb 10, 2018 8:22 pm
- Forum: Secondary Level
- Topic: Find Formula for Sequence
- Replies:
**2** - Views:
**1298**

### Find Formula for Sequence

Find a formula for $a_n$ satisfying $a_0=a_1=1$, and $a_n=2(a_{n-1}+a_{n-2})$, for all $n \geqslant 2$

- Fri Feb 09, 2018 10:50 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2015, problem 4
- Replies:
**1** - Views:
**5627**

### Re: APMO 2015, problem 4

Basically there are two possible approaches that I considered. Since the circle intersects at most $2n$ points in $A$, we want either (1) the circle to intersect all the lines in $A$ twice and the circle contains exactly one of the points of intersection between lines in $A$ or, (2) the circle inter...

- Fri Feb 09, 2018 10:38 pm
- Forum: Secondary Level
- Topic: combinatorics
- Replies:
**20** - Views:
**5867**

### Re: combinatorics

Let $5$ members be common for all $9$ committees

So, the number of

Adding the VIP, the number of total members=$135+5=140$

**[Let they be called VIP]**So, the number of

**non-VIP**members of each committee is=$20-5=15$ and, in total=$15 \times 9=135$Adding the VIP, the number of total members=$135+5=140$