Search found 172 matches

by Zzzz
Thu Dec 09, 2010 2:00 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO H.Sec 2010. Problem 10
Replies: 2
Views: 2577

BdMO H.Sec 2010. Problem 10

আচ্ছা, আমি কখনোই ১০ নম্বর সমস্যাটার সমাধান কোথাও দেখি নাই। নিজেও করতে পারি নাই অবশ্যই। কেউ কি দিতে পারেন? সমস্যাটা হইলঃ Let $a_1,a_2,…,a_k,…,a_n$ is a sequence of distinct positive real numbers such that $a_1<a_2<…<a_k$ and $a_k>a_{k+1}>…>a_n$ . A grasshopper is to jump along the real axis, starting...
by Zzzz
Thu Dec 09, 2010 1:37 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO Higher secondary solutions
Replies: 13
Views: 10538

Re: BdMO Higher secondary solutions

আচ্ছা, ৮,৯ নম্বরের সমাধান আগেও দেখছি। কিন্তু আমি কখনোই ১০ নম্বর সমস্যাটার সমাধান কোথাও দেখি নাই। নিজেও করতে পারি নাই অবশ্যই। কেউ কি দিতে পারেন? সমস্যাটা হইলঃ Let $a_1,a_2,…,a_k,…,a_n$ is a sequence of distinct positive real numbers such that $a_1<a_2<…<a_k$ and $a_k>a_{k+1}>…>a_n$. A grasshopper is ...
by Zzzz
Thu Dec 09, 2010 1:19 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO 2005-4
Replies: 10
Views: 5593

Re: Imo 2005-4

Probably the problem statement should be: Determine all positive integers such that they are coprime to all the terms of this sequence \[a_n=2^n+6^n+3^n-1^n, \forall n \in N\] আর যে এই সমস্যার সমাধান একবার দেখছে তার ভোলার কথা না :P আমি খালি সমাধান মনে করে লিখতেছি না, কেউ যদি এখন সমাধান করে তাহলে সে ...
by Zzzz
Thu Dec 09, 2010 7:25 am
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10904

Re: Geometry Marathon v1.0

Problem# 4 $P$ is a point in the interior of $\Delta ABC$. The three lines through $P$ parallel to the sides of the triangle divide the triangle into three parallelograms and three triangles. Prove that, the perimeter of each of the three small triangles is equal to the length of the adjacent side ...
by Zzzz
Thu Dec 09, 2010 6:51 am
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10904

Re: Geometry Marathon v1.0

Let the circumcenter is $O$. $AO$ intersects the perpendicular line at $U$ at point $X$. Extended $AU$ meets circumcircle at $Y$. So, $Y$ is the midpoint of arc $BC$ and $OY\perp BC$. From $\Delta OAY, OA=OY$. So, \[\angle OAY=\angle OYA\] Again, $UX\parallel OY$. So, \[\angle OYA= \angle XUA\] \[\R...
by Zzzz
Wed Dec 08, 2010 5:20 pm
Forum: Computer Science
Topic: Is math essential for programming?
Replies: 11
Views: 6017

Re: Is math essential for programming?

Hi, I don't know much about which fields are needed. Now, I practice algorithms only for solving that kind of problems which are appropriate for contests like IOI(International Olympiad in Informatics). Here is something like syllabus for IOI (http://people.ksp.sk/~misof/ioi-syllabus/). You can down...
by Zzzz
Wed Dec 08, 2010 12:25 pm
Forum: Algebra
Topic: Find value using the roots of polynomial
Replies: 5
Views: 3498

Re: Find value using the roots of polynomial

Ow... sorry. Actually its painful :P I will write formal solutions from now :)
by Zzzz
Wed Dec 08, 2010 10:14 am
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10904

Re: Geometry Marathon v1.0

Ops.. I can't remember a cute problem :( Try this easy one and give a solution with a problem :) Problem 2: In a triangle $ABC, \angle ACB= 90^{\circ}. BC>AC.$ The perpendicular bisector of $AB$ intersects $BC$ at $D$ and $AC$ at $E$. $DE=AB$. Find $\angle ABC$ [Mod Edit: Write problem number before...
by Zzzz
Wed Dec 08, 2010 10:04 am
Forum: Algebra
Topic: Find value using the roots of polynomial
Replies: 5
Views: 3498

Re: Find value using the roots of polynomial

Just use $\sum\alpha=0, \sum\alpha\beta=-1, \alpha\beta\gamma=1$ ;)
by Zzzz
Wed Dec 08, 2010 9:47 am
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10904

Re: Geometry Marathon v1.0

I have got a solution. I have used some identities. Here are the identities: i) The inradius of an equilateral triangle, $r=\frac{\sqrt{3}}{6} a$, here $a$ is the length of each side. ii) If $ABC$ is a triangle and the excircle on side $BC$ touches $AB$ at $D$ then $AD=s$. iii) If $ABC$ is a triangl...