Search found 172 matches

by Zzzz
Mon Feb 07, 2011 3:06 pm
Forum: National Math Olympiad (BdMO)
Topic: problem of nmo 2010 secondary
Replies: 2
Views: 1725

Re: problem of nmo 2010 secondary

moved the topic. please choose the right forum for posting problems (read about the rules here)
by Zzzz
Mon Feb 07, 2011 3:05 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4641

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 :)
by Zzzz
Mon Feb 07, 2011 1:13 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4641

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...
by Zzzz
Mon Feb 07, 2011 10:40 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2007/8
Replies: 5
Views: 2544

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.
by Zzzz
Mon Feb 07, 2011 10:33 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2007/9
Replies: 10
Views: 4641

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 $\sqrt 2$ ?
by Zzzz
Fri Feb 04, 2011 10:30 am
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2008/functional equation
Replies: 1
Views: 1783

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...
by Zzzz
Wed Feb 02, 2011 8:04 pm
Forum: Combinatorics
Topic: Moon vai iz gonna to hack my acount :x :x
Replies: 11
Views: 5319

Re: Moon vai iz gonna to hack my acount :x :x

yap! I thought zubaer vai did $\frac{1}{10^{10}}\times 25$ but, i was wrong! ... Hey.. I actually did it :P Look, think about this problem: there are $5$ vowels, what is the probability that if I pick one, it will be $a$? Answer is obvious (though its a dangerous word in mathematics :| ) $\frac {1}...
by Zzzz
Wed Feb 02, 2011 1:51 pm
Forum: Combinatorics
Topic: Moon vai iz gonna to hack my acount :x :x
Replies: 11
Views: 5319

Re: Moon vai iz gonna to hack my acount :x :x

হুম, আমারও তো তাই আসলো :roll:
by Zzzz
Wed Feb 02, 2011 8:15 am
Forum: Physics
Topic: পানির পাত্রে পিন ফুটালে কী হয়?
Replies: 10
Views: 4375

Re: পানির পাত্রে পিন ফুটালে কী হয়?

একটা ব্যাপার তো সহজেই বুঝা যায় যে পানি বের হওয়ার হার ছিদ্রের ক্ষেত্রফলের সমানুপাতিক ধরণের হবে :? কারণ মনে করা যাক একটা পাত্রের নিচে পুরাটাই খুলে দিলাম, তরল পদার্থ মুহুর্তের মাঝে নাই হয়ে যাবে। কিন্তু ছোট ছিদ্র করলে অনেকক্ষণ ধরে পড়বে। ছিদ্র ছোট হইলে বেগ বেশি হবে সেইটা ঠিক আছে, তবে তরল কম বের হবে। ...
by Zzzz
Tue Feb 01, 2011 9:19 am
Forum: Combinatorics
Topic: Moon vai iz gonna to hack my acount :x :x
Replies: 11
Views: 5319

Re: Moon vai iz gonna to hack my acount :x :x

মুন ভাইয়ার দোররা খাওয়ার সফলতার সম্ভাবনা দেখা যাচ্ছে খুবই কম... $\frac {25} {10^{10}}$