Search found 185 matches
- Sun Aug 07, 2016 10:19 am
- Forum: Number Theory
- Topic: IMO Shortlist 2012 N1
- Replies: 7
- Views: 5498
Re: IMO Shortlist 2012 N1
OK. I have approached it like this. Let, $d= gcd(m,n).$ If, $d > 1$, if $d|x$ & $ d|y $ then $d|x^2+kxy+y^2 $ for all k.So,though the multiple of d satisfies condition, but $A \ne \mathbb{Z}$. here it is easy to see, $ d=1$ . Now,We let,the set $A$ is admissible containing m,n.So,if $ x^2 \in A$ , ...
- Fri Aug 05, 2016 8:26 pm
- Forum: Combinatorics
- Topic: Guide the rook
- Replies: 1
- Views: 2477
Re: Guide the rook
Hint:
- Fri Aug 05, 2016 7:53 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2016 #4
- Replies: 2
- Views: 7234
Re: APMO 2016 #4
I think, the answer is $57$.(may be). According to condition, we can make a cycle of $57$ cities where it is always possible to have a reach-connection between any two cities using at most $28$ flights . So,any $2$ of those $57$ cities cannot situate in the same group. So, at least $57$ groups are ...
- Fri Aug 05, 2016 2:07 pm
- Forum: Geometry
- Topic: Circumcircle is tangent to the circumcircle
- Replies: 2
- Views: 2774
- Fri Aug 05, 2016 12:35 pm
- Forum: Site Support
- Topic: Visual problems with align code
- Replies: 3
- Views: 9989
Re: Visual problems with align code
Well, I don't see any overlapping. It's just fine.
- Wed Aug 03, 2016 11:36 am
- Forum: Combinatorics
- Topic: Canada 2007
- Replies: 1
- Views: 2233
- Thu Jul 28, 2016 11:18 pm
- Forum: Secondary Level
- Topic: 2014-national
- Replies: 15
- Views: 11815
Re: 2014-national
This isn't obvious. You have to prove it. (This isn't even true for a $2\times 2$ chessboard.)RJHridi wrote: So the maximum number of knights placed in the board will be the number of black or white squares, assuring that none attacks anyone.
- Thu Jul 28, 2016 10:26 pm
- Forum: Geometry
- Topic: Incenter of Triangle
- Replies: 2
- Views: 3155
Re: Incenter of Triangle
Take the triange $ABC$ for which it attains the minimum value.Consider the case when $CA\neq CB$. Now let $CI$ meets the incirle at $D$ so that $I$ lies between $C$ and $D$. Let the tangent at $D$ meet $AI,BI$ at $A_0,B_0$ resp. Then prove that $AI+BI \geq A_0+B_0$(You will need to go through some m...
- Thu Jul 28, 2016 9:56 pm
- Forum: Higher Secondary Level
- Topic: ordered pair (n,r)
- Replies: 1
- Views: 2710
Re: ordered pair (n,r)
You can use the well known fact that $\frac{n}{gcd(n,k)} \mid \binom{n}{k} \text{ } \forall n,k\in \mathbb{N}$ with $k\leq n$.jagdish wrote:Total number of whole number integer ordered pair $(n,r)$ in $\displaystyle \binom{n}{r} = 120$
- Tue May 31, 2016 5:04 pm
- Forum: Combinatorics
- Topic: even odd even odd
- Replies: 7
- Views: 5794
even odd even odd
A $2015\times 2015$ grid is coloured like a chessboard so that the four corner squres are coloured black. We put pebbles in some of the cells so that every row and column contains an odd number of cells with pebbles. Prove that there are an even number of white cells with pebbles.