Search found 183 matches

by asif e elahi
Mon Feb 15, 2016 8:48 am
Forum: National Math Olympiad (BdMO)
Topic: BDMO national higher secondery -prb 07
Replies: 2
Views: 2071

Re: BDMO national higher secondery -prb 07

Assume triangles $COB,COA,AOB$ have area $p,q,r$ respectively. Then express every ratio in terms of $p,q,r$.
by asif e elahi
Fri Feb 05, 2016 11:29 pm
Forum: Primary Level
Topic: Divisional Math Olympiad, Dhaka-2016,primary, ques. 7
Replies: 10
Views: 6330

Re: Divisional Math Olympiad, Dhaka-2016,primary, ques. 7

ahsaf wrote:I didn't understand why are we taking $99$ to prove the problem
Because $x$ has the only value $99$.
by asif e elahi
Wed Feb 03, 2016 12:36 pm
Forum: Junior Level
Topic: Easy Chess Tournament Problem
Replies: 1
Views: 1221

Re: Easy Chess Tournament Problem

Let $A,B,C$ be the set of first $3$,middle $4$ and last $5$ players respectively according to their rank and $U$ is the union set.Let $f(X,Y)$ denote the total score gained by the players of set $X$ against players of set $Y$.Easy to see that every match has total outcome of point $1$. now $f(A,U)=f...
by asif e elahi
Sun Jan 31, 2016 4:03 pm
Forum: Primary Level
Topic: Divisional Math Olympiad, Dhaka-2016,primary, ques. 7
Replies: 10
Views: 6330

Re: Divisional Math Olympiad, Dhaka-2016,primary, ques. 7

The condition gives us the equation $x+\frac{y}{100}=y-\frac{x}{100}$. Then prove that $x=99$.
by asif e elahi
Mon Jan 25, 2016 10:46 pm
Forum: Secondary Level
Topic: 2014-national
Replies: 15
Views: 5150

Re: 2014-national

seemanta001 wrote:The solution is:
For an $m \times n$ chessboard, the number of the knights is $n \times \lceil\dfrac{m}{3}\rceil$.
Can you please explain your solution??
by asif e elahi
Mon Jan 25, 2016 10:32 pm
Forum: Geometry
Topic: A BEAUTIFUL GEO
Replies: 1
Views: 1173

Re: A BEAUTIFUL GEO

Take point $P'$ on ray $OQ$ so that $QB.QD=QO.QP=QE.QC$ where $Q=BD\cap CE$. Then $BODP'$ and $COEP'$ are cyclic.After some easy angle chasing, it can be shown that $\angle BP'C= \angle BAC=\angle EP'D$ which makes $ACBP'$ and $ADEP'$ cyclic. So $P'\equiv P$. The rest is easy.
by asif e elahi
Mon Jan 25, 2016 9:33 pm
Forum: Divisional Math Olympiad
Topic: Dhaka regional higher secondary/8
Replies: 3
Views: 1984

Re: Dhaka regional higher secondary/8

Prove that if $5 \nmid x$, then $f(x)=0$ using the first 2 conditions.
by asif e elahi
Mon Jan 25, 2016 9:04 pm
Forum: Divisional Math Olympiad
Topic: Dhaka regional 2015 secondary/4
Replies: 2
Views: 1496

Re: Dhaka regional 2015 secondary/4

Prove $ABCD$ is a square using spiral similarity.
by asif e elahi
Mon Jan 25, 2016 8:54 pm
Forum: Social Lounge
Topic: A frequently asked question (FAQ)
Replies: 3
Views: 1899

Re: A frequently asked question (FAQ)

Of course. But set square is not allowed in IMO.
by asif e elahi
Sun Jan 10, 2016 10:40 pm
Forum: Geometry
Topic: Chinese Girls' Mathematical Olympiad 2015,P1
Replies: 4
Views: 1902

Re: Chinese Girls' Mathematical Olympiad 2015,P1

Let $P$ be the reflection of $A$ across $D$. Then prove that $ \triangle DEF \cup M \sim \triangle CAP \cup D.$