Search found 24 matches
- Sat Jan 19, 2019 8:46 pm
- Forum: Combinatorics
- Topic: ISL 2010 C2
- Replies: 1
- Views: 5714
ISL 2010 C2
On some planet, there are $2^N$ countries $(N\geq 4)$.Each country has a flag $N$ units wide and $1$ unit high composed of $N$ fields of size $1\times1$, each field being either $Yellow$ or $Blue$.No two countries have the same flag.We say that a set of $N$ flags is $DIVERSE$ if these flags can be a...
- Sat Apr 14, 2018 12:43 pm
- Forum: Combinatorics
- Topic: Football and Combi
- Replies: 3
- Views: 7203
Re: Football and Combi
why?samiul_samin wrote: ↑Fri Apr 13, 2018 9:54 pmIt is not possible if any of the referees is not same weighted.
- Thu Apr 12, 2018 2:32 pm
- Forum: Combinatorics
- Topic: Football and Combi
- Replies: 3
- Views: 7203
Football and Combi
$23$ people, each with integral weight,decide to play football, separating into two teams of $11$ people and a referee.To keep things fair, the teams chosen must have the equal total weight.It turns out that no matter who is chosen to be the referee, this can always be done.Prove that the $23$ peopl...
- Tue Mar 13, 2018 6:36 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary/Higher Secondary 2018/6
- Replies: 3
- Views: 3543
Re: BdMO National Higher Secondary 2018#6
$3(m^2+n^2)- 7(m+n) =-4$ Substitute $(m+n)=x$ and $(m^2+n^2)=y$ So, $7x-3y=4$ and the general solution of this diophantine equation is $x=3k+1$, $y=7k+1$ where $k$ is an integer. So, $(m+n)=3k+1$............$(1)$ $(m^2+n^2)=7k+1$...........$(2)$ From $(2)$ we get that $m^2+n^2=7k+1$ or,$[(m+n)^2 +(m...
- Tue Mar 13, 2018 5:33 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary/Higher Secondary 2018/3
- Replies: 2
- Views: 2765
Re: BdMO National Higher Secondary 2018#3
The ans. is $18$
- Sat Dec 16, 2017 12:39 am
- Forum: Number Theory
- Topic: Prime numbers
- Replies: 4
- Views: 6921
Re: Prime numbers
use parity.
- Fri Sep 22, 2017 5:58 pm
- Forum: Divisional Math Olympiad
- Topic: BdMO 2017 : Dhaka
- Replies: 3
- Views: 3739
BdMO 2017 : Dhaka
How many ways can 100000 be written as the product of three positive integers?
- Sun Jul 30, 2017 11:35 am
- Forum: Combinatorics
- Topic: need the solution
- Replies: 5
- Views: 8126
Re: need the solution
I think it is $ \frac {102.101}{ 2} $. Notice if you get o in physics then you will have only one way to get 200 marks in the three subjects.if you get 1 in physics then you will have 2 ways and for 2 you will have 3 ways and it will go on for o to 100 ..It forms a series that $ 1+2+3+.............+...
- Sun Jul 30, 2017 11:03 am
- Forum: Number Theory
- Topic: Beautifull divisibility
- Replies: 1
- Views: 2523
Re: Beautifull divisibility
$ab^2+b+7 |a^2b+a+b$ $Case\ 1: when \ a<b$ from divisibility inequality we know that, $a^2b+a+b \geq ab^2+b+7$ or, $ab(a-b) \geq 7-a$ or, $a-7 \geq ab(b-a)$ it is clear that there is no solution for $a,b\ \epsilon\ N\ if\ a<b$ $ Case\ 2: when\ a=b$ $ ab(a-b)=7-a $ or, $ a(ab-b^2+1)=7 $ from that $ (...
- Fri Jun 30, 2017 2:28 pm
- Forum: Secondary Level
- Topic: Bdmo 2014 Mymensingh
- Replies: 0
- Views: 2345
Bdmo 2014 Mymensingh
Help me to solve these problems.....