Search found 73 matches

by Tasnood
Tue Feb 13, 2018 10:34 pm
Forum: Junior Level
Topic: Need a solution to my question please.
Replies: 1
Views: 3382

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...
by Tasnood
Tue Feb 13, 2018 8:47 pm
Forum: Secondary Level
Topic: secondary regional 2017
Replies: 2
Views: 2791

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
by Tasnood
Tue Feb 13, 2018 8:33 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO 2017 National Round Secondary 7
Replies: 13
Views: 3135

Re: BdMO 2017 National Round Secondary 7

$K$ may not be $2$
by Tasnood
Tue Feb 13, 2018 8:27 pm
Forum: Site Support
Topic: Regional Olympiad 2016
Replies: 3
Views: 11323

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...
by Tasnood
Tue Feb 13, 2018 7:47 pm
Forum: Secondary Level
Topic: Triangle geometry
Replies: 5
Views: 3665

Re: Triangle geometry

Do you want to mean "Joining $AD,BE,CF$"?
Then, they intersect at a single point, no triangle comes out. [If I don't miss anything]
by Tasnood
Sat Feb 10, 2018 11:55 pm
Forum: Secondary Level
Topic: Find Formula for Sequence
Replies: 2
Views: 768

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...
by Tasnood
Sat Feb 10, 2018 11:28 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO 2017 National Round Secondary 8
Replies: 2
Views: 1425

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-...
by Tasnood
Sat Feb 10, 2018 8:22 pm
Forum: Secondary Level
Topic: Find Formula for Sequence
Replies: 2
Views: 768

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 $n \geqslant 2$
by Tasnood
Fri Feb 09, 2018 10:50 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2015, problem 4
Replies: 1
Views: 5074

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...
by Tasnood
Fri Feb 09, 2018 10:38 pm
Forum: Secondary Level
Topic: combinatorics
Replies: 20
Views: 3138

Re: combinatorics

Let $5$ members be common for all $9$ committees [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=$135+5=140$