Search found 217 matches

by zadid xcalibured
Mon Feb 18, 2013 3:52 pm
Forum: Algebra
Topic: VNMO 2013
Replies: 3
Views: 1677

Re: VNMO 2013

Define the function $f(x)=\frac{x+2}{2^x}$
$f'(x)=2^{-x}$ $(1-(x+2) ln2)$.
As $x>1$,$f'(x)<2^{-x}(1-ln8)<0$
so this function is decreasing.
Which implies the sequence $a_n$ is increasing.
Now by induction we can show that $a_n \leq 2$ for all $n$.
actually this is the limit.
by zadid xcalibured
Mon Feb 11, 2013 10:11 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 8
Replies: 6
Views: 3560

Re: BdMO 2013 Higher Secondary Problem 8

$A$,$X$,$C$,$Y$ cyclic.And $Z$,$X$,$S$,$Y$ cyclic.So $EZ.ES$=$EX.EY$=$EA.EC$ Let $H$ be the orthocentre.$EA.EC=EH.EB$ But $ES.EZ=EH.EB$ so $H$ is the orthocentre of $\triangle ZBS$ So $ZH$ is perpendicular to $BS$. Let $M$ be the midpoint of $AC$. $ZH$ is the polar of $B$ with respect to circle $AFD...
by zadid xcalibured
Sat Feb 02, 2013 12:07 am
Forum: Algebra
Topic: Fuctional inequality
Replies: 1
Views: 1193

Re: Fuctional inequality

Telescoping yields an elegant solution. :D
by zadid xcalibured
Fri Feb 01, 2013 10:52 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 8
Replies: 10
Views: 4948

Re: BdMO National 2012: Secondary 8

That's what stops the good ninja(me).Mis-comprehension of problem statement.
Now i know how the hell u deduce those things. :twisted:
by zadid xcalibured
Fri Feb 01, 2013 10:23 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 8
Replies: 10
Views: 4948

Re: BdMO National 2012: Secondary 8

I don't know how the hell you deduced $EA=EE"$
Because that implies $\angle E'AE"$ $=90 ^\circ$ which is not true.
by zadid xcalibured
Fri Feb 01, 2013 10:04 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 8
Replies: 10
Views: 4948

Re: BdMO National 2012: Secondary 8

I don't know how the hell you deduced that $\angle ECA=2\angle EAC$.Please explain.
Your solution is incorrect.
by zadid xcalibured
Thu Jan 31, 2013 7:11 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO Higher secondary solutions
Replies: 13
Views: 10568

Re: BdMO Higher secondary solutions

TIUrmi wrote:ইতিহাসে আমার নাম স্বর্ণাক্ষরে লেখা থাকবে সেই আনন্দে আমার কান্না পাচ্ছে। :cry:
এই কথা পড়ে আমার হাসি পাচ্ছে। :mrgreen:
by zadid xcalibured
Wed Jan 30, 2013 2:30 pm
Forum: Divisional Math Olympiad
Topic: Rajshahi MO 2013, Secondary 1
Replies: 9
Views: 3803

Re: Rajshahi MO 2013, Secondary 1

Oi Mahi,that makes use of such a big assumption as for those $4$ points ,the diagonals intersect strictly inside the hull.But we can get $3$ intersection points.Namely for points $A$,$B$,$C$,$D$ ,$AB \cap CD$ ,$AD \cap BC$ and $AC \cap BD$.
by zadid xcalibured
Sat Jan 26, 2013 12:16 am
Forum: Primary Level
Topic: palindrome number
Replies: 5
Views: 6442

Re: palindrome number

Prosenjit,
Your solution is close to brute force.you have to show that 11 must divide them.Eventually in order to be a perfect square 121 must divide them.Which is not possible.
by zadid xcalibured
Fri Jan 25, 2013 11:31 pm
Forum: Geometry
Topic: Geometry Marathon v1.0
Replies: 23
Views: 10955

Re: Geometry Marathon v1.0

I like this marathon.I am so glad that i am posting in the same marathon as our predecessors. :D
Why don't we run this marathon?