Search found 65 matches

by Absur Khan Siam
Wed Mar 07, 2018 6:28 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 612

Re: BdMO National Higher Secondary 2014/6

samiul_samin wrote:
Mon Mar 05, 2018 11:54 pm
Absur Khan Siam wrote:
Mon Mar 05, 2018 11:27 pm
Sorry, the solution above is wrong. I will edit it as soon as possible.(as I can't delete it now)
Is my solution also wrong?
Not yours, my one was wrong.(now edited)
by Absur Khan Siam
Mon Mar 05, 2018 11:27 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 612

Re: BdMO National Higher Secondary 2014/6

Sorry, the solution above is wrong. I will edit it as soon as possible.(as I can't delete it now)
UPD: : solution edited.
by Absur Khan Siam
Mon Mar 05, 2018 11:16 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2014/6
Replies: 6
Views: 612

Re: BdMO National Higher Secondary 2014/6

Let us construct a directed graph $T$ consisting $n$ nodes where each node represents a player. An edge $x \rightarrow y$ represent player $x$ has lost $y$. Thus, this graph consists of $\binom{n}{2}$ edges. "The players can be labeled $1,2,.......,n$ so that $i$ beats $i+1$" is equivalent to "The g...
by Absur Khan Siam
Mon Mar 05, 2018 10:52 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 5
Replies: 15
Views: 1970

Re: BDMO 2017 National round Secondary 5

Tasnood wrote:
Mon Mar 05, 2018 10:34 pm
Sorry for Interrupt. My answer was same of #Nahin but this solution is new to me.
How can we find the radius of two circles same?
$AC = AB$ , radius of the $\widehat{BC}$
$BC = AB$ , radius of the $\widehat{AB}$

Thus, $AC = BC$
by Absur Khan Siam
Sat Feb 10, 2018 10:59 pm
Forum: Secondary Level
Topic: Find Formula for Sequence
Replies: 2
Views: 265

Re: Find Formula for Sequence

It is a linear recurrence relation.You can derive the formula of $a_n$ by solving this recurrence relation.
by Absur Khan Siam
Sun Feb 04, 2018 11:17 pm
Forum: Geometry
Topic: EGMO 2013/1
Replies: 2
Views: 470

Re: EGMO 2013/1

Applying Apollonius's theorem to $\triangle ABD$ , $AB^2 + AD^2 = 2AC^2 + 2BC^2 \cdots (i)$ Applying Stuart's theorem to $\triangle BCE$ , $CE(AB^2 + AC.CE) = BE^2.AC + BC^2.AE \cdots (ii) \Rightarrow 3AB^2 + 6AC^2 = AD^2 + 2BC^2$ $(i) + (ii)$ $\Rightarrow 4AB^2 + 4AC^2 = 4BC^2 \Rightarrow AB^2 + A...
by Absur Khan Siam
Sun Feb 04, 2018 11:08 pm
Forum: Geometry
Topic: EGMO 2013/1
Replies: 2
Views: 470

EGMO 2013/1

The side $BC$ of $\triangle ABC$ is extended beyond $C$ to $D$ so that $CD = BC$.The side $CA$ is extended beyond $A$ to $E$ so that $AE = 2CA$.
Prove that if $AD = BE$, then $\triangle ABC$ is right-angled.
by Absur Khan Siam
Sun Feb 04, 2018 12:34 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 1
Replies: 19
Views: 2464

Re: BDMO 2017 National round Secondary 1

My solution may be wrong.But the $20$ cases yield to a result that both team have a probability of $\frac{1}{2}$ to win the series.
by Absur Khan Siam
Sat Feb 03, 2018 11:16 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 1
Replies: 19
Views: 2464

Re: BDMO 2017 National round Secondary 1

Here are the list of all possibilities of the result of the game(Denoting $W$ and $L$ are the win and lose of Bangladesh): $WWW$ $LLL$ $LWWW$ $WLWW$ $WWLW$ $WLLL$ $LWLL$ $LLWL$ $WWLLW$ $WLWLW$ $WLLWW$ $LWWLW$ $LWLWW$ $LLWWW$ $WWLLL$ $WLWLL$ $WLLWL$ $LWWLL$ $LWLWL$ $LLWWL$ Hence there are $20$ differ...
by Absur Khan Siam
Sat Feb 03, 2018 12:40 pm
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 6
Replies: 9
Views: 1318

Re: BDMO 2017 National round Secondary 6

Tasnood wrote:
Fri Feb 02, 2018 11:11 pm
Right this time?
Yah, I think so...