Search found 172 matches

Mon Feb 07, 2011 3:06 pm
Topic: problem of nmo 2010 secondary
Replies: 2
Views: 1669

Re: problem of nmo 2010 secondary

Mon Feb 07, 2011 3:05 pm
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4516

Re: BdMO National Higher Secondary 2007/9

draw segments and guess the shape. try to prove your assumption... try it yourself, it will be fun
Mon Feb 07, 2011 1:13 pm
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4516

Re: BdMO National Higher Secondary 2007/9

How can you be sure that $L$ is a square? See the image below. The Blue lines are some segments that have length $2$ and whose endpoints are on adjacent side of the square. $S$ is the set of all such segments. Join the midpoints of the segments and find out the shape of the area enclosed by the midp...
Mon Feb 07, 2011 10:40 am
Topic: BdMO National Higher Secondary 2007/8
Replies: 5
Views: 2469

Re: BdMO National Higher Secondary 2007/8

photon wrote:...
How much a chord goes near to the center parallel to its previous position,it is increased in both sides equally.
...
Sorry, its wrong Its better if you try to find some logical solution. Sometimes some properties seem obvious to us, but don't believe those until you get a proof.
Mon Feb 07, 2011 10:33 am
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4516

Re: BdMO National Higher Secondary 2007/9

photon wrote:$\sqrt{2}$ is the length of the segments by the mid-points.
So the area is 2...
How have you got that $L$ will be a square of side length $\sqrt 2$ ?
Fri Feb 04, 2011 10:30 am
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2008/functional equation
Replies: 1
Views: 1741

Re: APMO 2008/functional equation

Hint goes first: Find the values of $f(1),f(2),f(3),...,f(16)$. It is easy to 'see' the sets $L,E,G$ and values of $a_k$s. Now prove using induction or contradiction :) Solution: (a) Notice that $L,G,E$ are mutually disjoint sets. Let $n$ is an even number $n=2k,\ k>0$ Now,$2f(k)<2f(k)+k$ \[\Right...
Wed Feb 02, 2011 8:04 pm
Forum: Combinatorics
Topic: Moon vai iz gonna to hack my acount :x :x
Replies: 11
Views: 5189