Search found 172 matches

by Zzzz
Mon Feb 13, 2012 8:25 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Higher Secondary 02
Replies: 11
Views: 2798

Re: BdMO National 2012: Higher Secondary 02

sm.joty wrote: ....

অর্থাৎ ১ম এ একবারে ১১ টা পার হবে তারপর ১ টা। ১ ভাবে।
২য় ক্ষেত্রে প্রথম ১০ টা একবারে তারপর বাকি ২ টা যাওয়া যায় ২ ভাবে।
৩য় ক্ষেত্রে প্রথম ৯ টা একবারে তারপর বাকি ৩ টা যাওয়া যায় ৩ ভাবে।

....
লাল অংশটা এবং সাথে এর পরে যা যা ধরস (৪টা ৪ ভাবে, ৫টা ৫ ভাবে... ) এইগুলা ভুল হইসে।
by Zzzz
Sun Feb 12, 2012 1:59 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Primary 10
Replies: 1
Views: 936

BdMO National 2012: Primary 10

Problem 10:
Tusher chose some consecutive numbers starting from $1$. He noticed that the least common multiple of those numbers is divisible by $100$. What is the minimum number of numbers he chose?
by Zzzz
Sun Feb 12, 2012 1:56 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Primary 6
Replies: 1
Views: 926

BdMO National 2012: Primary 6

Problem 6: Consider the given diagram. There are three rectangles shown here. Their lengths are $3,\ 4$ and $5$ units respectively, widths respectively $2,\ 3$ and $4$ units. Each small grid represents a square $1$ unit long and $1$ unit wide. Use these diagrams to find out the sum of the consecuti...
by Zzzz
Sun Feb 12, 2012 1:52 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Primary 5
Replies: 3
Views: 1317

BdMO National 2012: Primary 5

Problem 5: If a number is multiplied with itself thrice, the resultant is called its cube. For example: $3 × 3 × 3 = 27$, hence $27$ is the cube of $3$. If $1,\ 170$ and $387$ are added with a positive integer, cubes of three consecutive integers are obtained. What are those three consecutive integ...
by Zzzz
Sun Feb 12, 2012 1:50 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Primary 4
Replies: 8
Views: 2617

BdMO National 2012: Primary 4

Problem 4:
Write a number in a paper and hold the paper upside down. If what you get is exactly same as the number before rotation then that number is called beautiful. Example: $986$ is a beautiful number. Find out the largest $5$ digit beautiful number.
by Zzzz
Sun Feb 12, 2012 1:20 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Primary 1
Replies: 8
Views: 2756

BdMO National 2012: Primary 1

Problem 1:
Find a three digit number so that when its digits are arranged in reverse order and added with the original number, the result is a three digit number with all of its digits being equal. In case of two digit numbers, here is an example: $23+32=55 $
by Zzzz
Sun Feb 12, 2012 9:32 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 10
Replies: 3
Views: 1407

BdMO National 2012: Junior 10

Problem 10:
The $n$-th term of a sequence is the least common multiple (l.c.m.) of the integers from $1$ to $n$. Which term of the sequence is the first one that is divisible by $100$?
by Zzzz
Sun Feb 12, 2012 9:29 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 9
Replies: 2
Views: 1340

BdMO National 2012: Junior 9

Problem 9:
Given triangle $ABC$, the square $PQRS$ is drawn such that $P,\ Q$ are on $BC,\ R$ is on $CA$ and $S$ is on $AB$. Radius of the triangle that passes through $A,\ B,\ C$ is $R$. If $AB = c,\ BC = a,\ CA = b,$ Show that $\frac{AS}{SB}=\frac{bc}{2aR}$
by Zzzz
Sun Feb 12, 2012 9:22 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 7, Primary 9
Replies: 2
Views: 1289

BdMO National 2012: Junior 7, Primary 9

Problem: Each room of the Magic Castle has exactly one door. The rooms are designed such that when you can go from one room to the next one through a door, the second room's length is equal to the first room's width, and the second room's width is half of the first room's width (see the figure). Ea...
by Zzzz
Sun Feb 12, 2012 9:12 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 6
Replies: 4
Views: 1536

BdMO National 2012: Junior 6

Problem 6:
In triangle $ABC$, $AB=7,\ AC=3,\ BC=9$. Draw a circle with radius $AC$ and center $A$. What is the distance from $B$ to the point on the circle that is furthest from $B$?