Search found 134 matches

by BdMO
Fri Jan 10, 2014 2:02 am
Forum: Geometry
Topic: BdMO National Olympiad 2013: Problemsets
Replies: 4
Views: 30208

Re: BdMO National Olympiad 2013: Problemsets

Bangladesh National Mathematical Olympiad 2013 : Higher Secondary Problem 1: A polygon is called degenerate if one of its vertices falls on a line that joins its neighboring two vertices. In a pentagon $ABCDE$, $AB=AE$, $BC=DE$, $P$ and $Q$ are midpoints of $AE$ and $AB$ respectively. $PQ||CD$, $BD...
by BdMO
Fri Jan 10, 2014 2:00 am
Forum: Geometry
Topic: BdMO National Olympiad 2013: Problemsets
Replies: 4
Views: 30208

Re: BdMO National Olympiad 2013: Problemsets

Bangladesh National Mathematical Olympiad 2013 : Secondary Problem 1: If $f: \mathbb R \mapsto \mathbb R$ is a function such that $f(x)=-f(-x)=f(x+1)$ for all real $x$, then what is the value of $f(2013)$? http://www.matholympiad.org.bd/forum/viewtopic.php?f=13&t=2921 Problem 2: A polygon is called...
by BdMO
Fri Jan 10, 2014 1:58 am
Forum: Geometry
Topic: BdMO National Olympiad 2013: Problemsets
Replies: 4
Views: 30208

Re: BdMO National Olympiad 2013: Problemsets

Bangladesh National Mathematical Olympiad 2013: Junior Problem $1$ : Nazia’s mobile phone has a strange problem. Each time she sends an SMS, it is also sent to all the existing numbers of her call list. The actual recipient of the SMS is then added to her call list.. At some point, Nazia deleted he...
by BdMO
Fri Jan 10, 2014 1:56 am
Forum: Geometry
Topic: BdMO National Olympiad 2013: Problemsets
Replies: 4
Views: 30208

BdMO National Olympiad 2013: Problemsets

Bangladesh National Mathematical Olympiad 2013: Primary Problem $1$ : A group of $7$ women takes $7$ days to make $7$ Nokshikatha. How many days will a group of $5$ women take for making $5$ Nokshikatha? http://www.matholympiad.org.bd/forum/viewtopic.php?f=13&t=2905 Problem $2$ : Nazia's mobile pho...
by BdMO
Fri Jan 10, 2014 1:45 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 10
Replies: 1
Views: 644

BdMO National 2013: Higher Secondary 10

$X$ is a set of $n$ elements. $P_m(X)$ is the set of all $m$ element subsets (i.e. subsets that contain exactly $m$ elements) of $X$. Suppose $P_m(X)$ has $k$ elements. Prove that the elements of $P_m(X)$ can be ordered in a sequence $A_1, A_2,...A_i,...A_k$ such that it satisfies the two conditions...
by BdMO
Fri Jan 10, 2014 1:44 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 8
Replies: 0
Views: 338

BdMO National 2013: Higher Secondary 8

$ABC$ is an acute angled triangle. Perpendiculars drawn from its vertices on the opposite sides are $AD$, $BE$ and $CF$. The line parallel to $DF$ through $E$ meets $BC$ at $Y$ and $BA$ at $X$. $DF$ and $CA$ meet at $Z$. Circumcircle of $XYZ$ meets $AC$ at $S$. Given, $\angle B=33^{\circ}$ find the ...
by BdMO
Fri Jan 10, 2014 1:43 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 5
Replies: 1
Views: 602

BdMO National 2013: Higher Secondary 5

Let $x>1$ be an integer such that for any two positive integers $a$ and $b$, if $x$ divides $ab$ then $x$ either divides $a$ or divides $b$. Find with proof the number of positive integers that divide $x$.
by BdMO
Fri Jan 10, 2014 1:42 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 4
Replies: 5
Views: 1292

BdMO National 2013: Higher Secondary 4

If the fraction $\dfrac{a}{b}$ is greater than $\dfrac{31}{17}$ in the least amount while $b<17$, find $\dfrac{a}{b}$.
by BdMO
Fri Jan 10, 2014 1:41 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 2
Replies: 2
Views: 690

BdMO National 2013: Higher Secondary 2

Let $g$ be a function from the set of ordered pairs of real numbers to the same set such that $g(x, y)=-g(y, x)$ for all real numbers $x$ and $y$. Find a real number $r$ such that $g(x, x)=r$ for all real numbers $x$.
by BdMO
Fri Jan 10, 2014 1:41 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Secondary 10, Higher Secondary 9
Replies: 2
Views: 963

BdMO National 2013: Secondary 10, Higher Secondary 9

Six points $A$, $B$, $C$, $D$, $E$, $F$ are chosen on a circle anticlockwise. None of $AB$, $CD$, $EF$ is a diameter. Extended $AB$ and $DC$ meet at $Z$, $CD$ and $FE$ at $X$, $EF$ and $BA$ at $Y$. $AC$ and $BF$ meets at $P$, $CE$ and $BD$ at $Q$ and $AE$ and $DF$ at $R$. If $O$ is the point of inte...