Search found 134 matches
- Fri Jan 10, 2014 1:15 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 5
- Replies: 1
- Views: 3058
BdMO National 2013: Primary 5
For any two numbers $x$ and $y$, the absolute value of $x$ and $y$ is defined as $|x-y| = $ difference between the numbers $x$ and $y$ . For example, $|5-2| = 3, |3-9| = 6$ . Let $a_1, a_2, a_3, \cdots , a_n$ be a sequence of numbers such that each term in the sequence is larger than the previous te...
- Fri Jan 10, 2014 1:14 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 4
- Replies: 3
- Views: 4097
BdMO National 2013: Primary 4
The English alphabets are arranged in $3$ rows in a Keyboard. Now somebody presses one key in the first row in such a way that there are same number of keys on both sides of that key in that row. Now a second person presses a key in the second row in the same way and a third person also does the sam...
- Fri Jan 10, 2014 1:13 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 3
- Replies: 3
- Views: 4070
BdMO National 2013: Primary 3
A cube-shaped room has six walls (floor, roof and east, west, north, south walls). A grasshopper is sitting at the south-west corner of the floor. The grasshopper needs to go to the north-east corner of the roof by jumping upward, northward or eastward and in each jump it goes one-third of the room'...
- Fri Jan 10, 2014 1:12 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 2, Junior 1
- Replies: 11
- Views: 11503
BdMO National 2013: Primary 2, Junior 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 her call list. The next SMS she sent was the $16^{th}$ SMS sent from her...
- Fri Jan 10, 2014 1:11 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 1
- Replies: 15
- Views: 15179
BdMO National 2013: Primary 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?
- Sat Feb 12, 2011 5:00 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/1
- Replies: 7
- Views: 5699
BdMO National Higher Secondary 2011/1
Problem 1:
Prove that for any non-negative integer $n$ the numbers $1, 2, 3, ..., 4n$ can be divided in tow mutually exclusive classes with equal number of members so that the sum of numbers of each class is equal.
Prove that for any non-negative integer $n$ the numbers $1, 2, 3, ..., 4n$ can be divided in tow mutually exclusive classes with equal number of members so that the sum of numbers of each class is equal.
- Sat Feb 12, 2011 4:59 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/2
- Replies: 7
- Views: 5617
BdMO National Higher Secondary 2011/2
Problem 2: In the first round of a chess tournament, each player plays against every other player exactly once. A player gets $3, 1$ or $-1$ points respectively for winning, drawing or losing a match. After the end of the first round, it is found that the sum of the scores of all the players is $90...
- Sat Feb 12, 2011 4:58 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/4
- Replies: 7
- Views: 5995
BdMO National Higher Secondary 2011/4
Problem 4:
Which one is larger 2011! or, $(1006)^{2011}$? Justify your answer.
Which one is larger 2011! or, $(1006)^{2011}$? Justify your answer.
- Sat Feb 12, 2011 4:57 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/5
- Replies: 4
- Views: 4081
BdMO National Higher Secondary 2011/5
Problem 5: In a scalene triangle $ABC$ with $\angle A = 90^{\circ}$, the tangent line at $A$ to its circumcircle meets line $BC$ at $M$ and the incircle touches $AC$ at $S$ and $AB$ at $R$. The lines $RS$ and $BC$ intersect at $N$ while the lines $AM$ and $SR$ intersect at $U$. Prove that the trian...
- Sat Feb 12, 2011 4:50 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/8
- Replies: 18
- Views: 11721
BdMO National Higher Secondary 2011/8
Problem 8: $ABC$ is a right angled triangle with $\angle A = 90^{\circ}$ and $D$ be the midpoint of $BC$. A point $F$ is chosen on $AB$. $CA$ and $DF$ meet at $G$ and $GB \parallel AD$. $CF$ and $AD$ meet at $O$ and $AF = FO$. $GO$ meets $BC$ at $R$. Find the sides of $ABC$ if the area of $GDR$ is ...