Search found 188 matches
- Fri Jan 27, 2012 7:32 pm
- Forum: Junior Level
- Topic: A train Journey
- Replies: 1
- Views: 1903
A train Journey
A train is coming from Dhaka to Chittagong,and the other train is travelling from Chittagong to Dhaka.Those two trains met on a spot.After the meeting,Dhaka-Chittagong going train needed 1 hour to reach Chittagong,and the Chittagong -Dhaka going train needed 4 hours to reach Dhaka.What is the ratio ...
- Fri Jan 27, 2012 12:47 pm
- Forum: Secondary Level
- Topic: Factorizing
- Replies: 5
- Views: 4204
Re: Factorizing
That's not a very hard thing.Dirichlet's theorem states that if $p$ is an odd prime, $a$ is a co-prime of it and let $b=(p-1)/2$, then $a^b\equiv 1(mod p)$ happens if $x^2\equiv a(mod p)$ has solution.If this modular equation doesn't have any solution, then $a^b\equiv -1(mod p)$.Proof of this theor...
- Fri Jan 27, 2012 12:35 pm
- Forum: Junior Level
- Topic: Mysterious(self-made)
- Replies: 6
- Views: 3789
Re: Mysterious(self-made)
What about,\[sin120^{\circ}\]
- Fri Jan 27, 2012 11:41 am
- Forum: Algebra
- Topic: Pythagorian triples
- Replies: 1
- Views: 1653
Re: Pythagorian triples
Hint:
- Thu Jan 26, 2012 8:17 pm
- Forum: Junior Level
- Topic: comparism
- Replies: 16
- Views: 9577
Re: comparism
I will give a very short and easy solution with the help of STIRLING'S APPROXIMATION.It says that,\[In(n!)\approx nIn(n)-n \]
Using this We get,\[300!\approx 1411.135\]
&\[In(100^{300})=300In100\approx 1381.551\]
So,$300!>100^{300}$
Using this We get,\[300!\approx 1411.135\]
&\[In(100^{300})=300In100\approx 1381.551\]
So,$300!>100^{300}$
- Thu Jan 26, 2012 7:39 pm
- Forum: Algebra
- Topic: An interesting Problem of Equation
- Replies: 3
- Views: 2372
Re: An interesting Problem of Equation
Plz edit your post.
- Thu Jan 26, 2012 7:37 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2011/4
- Replies: 2
- Views: 3013
Re: BdMO National Junior 2011/4
Let me, divide the set into 40 equivalent subset such that every subset consists of 4 consecutive numbers.Now initialize from the 1st subset.The subset is {1,2,3,4}.the next one is {5,6,7,8} every number of this subset differs 4 with previous one.Like that every element of a subset must differ with ...
- Thu Jan 26, 2012 7:15 pm
- Forum: Secondary Level
- Topic: Weighty Problem
- Replies: 7
- Views: 3906
Weighty Problem
Among 80 identical coins,every coin is of same weight except one coin.This coin is lighter.You are given a scale.But you have no weight(Batkhara).How will u identify the lighter coin measuring weight for just four times?
Lets see who solves first
Lets see who solves first
- Thu Jan 26, 2012 3:31 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2011/2
- Replies: 2
- Views: 3205
Re: BdMO National Junior 2011/2
In the triangle $ABC$ , $AD=DC=AC$ so,angle $ADC=60$ then angle $ADB=120$ if there is any other vertice equals to $BD$ then there there are total of the angles of triangle ABD greater than 180.so $AD=BD$.Now we can find those angels easily.which are 30,60 & 90.
- Thu Jan 26, 2012 2:54 pm
- Forum: Junior Level
- Topic: > Or <???
- Replies: 3
- Views: 2787
Re: > Or <???
Slip of Keyboard..