Search found 108 matches

by rah4927
Sun Apr 02, 2017 1:58 pm
Forum: Combinatorics
Topic: Finding a confirmed civilian among $n^2$ players in Mafia
Replies: 0
Views: 223

Finding a confirmed civilian among $n^2$ players in Mafia

$n^2$ players labelled $1,2,...,n^2$ were playing in a mafia game. There were $2n-3$ mafia in total. During the night phase, everyone asked the moderator a question about the status of some player (mafia or civilian) so that they can reveal this information in the day phase. During the day phase, pl...
by rah4927
Sat Apr 01, 2017 1:41 pm
Forum: Social Lounge
Topic: Petition to make Zaki Khalil overlord
Replies: 2
Views: 324

Re: Petition to make Zaki Khalil overlord

I agree - math camp is the perfect place for transferring of knowledge and skills -- we really could do with smn like zaki khalil - the current imo team members aren't doing well enough of a job compared to what he could do.

#Maki_Zaki_Great_Again
by rah4927
Fri Mar 31, 2017 10:11 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 3052

Re: Combi Marathon

Sketch of solution (with @ahmedittihad) : Partition $K_n$ into $\lfloor \frac{n-1}{2} \rfloor$ hamiltonian cycles. Since each cycle has length $n$, we can divide each cycle into two paths of length $i$ and $n-i$. This achieves the desired construction. The proof does need to be modified depending on...
by rah4927
Tue Mar 28, 2017 10:57 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 51
Views: 2985

Re: BDMO Forum Mafia #1

VOTE: thamimzahin. So he can die quickly.
by rah4927
Mon Mar 27, 2017 7:08 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 51
Views: 2985

Re: BDMO Forum Mafia #1

1. dshasan
2. ahmedittihad
3. Epshita32
4. Atony Roy Chowdhury
5. Raiyan Jamil
6. rah4927

Next user copy paste this and add your name at the end.
by rah4927
Thu Mar 23, 2017 2:12 am
Forum: Site Support
Topic: The Gonit IshCool Project
Replies: 3
Views: 431

Re: The Gonit IshCool Project

Hey zawad this is a great project and I would be happy to collaborate on this one. However, how do you propose students and mentors communicate with each other? Are you confident the PM system on the forum is good and friendly enough for users to communicate? There isn't a chat system which I feel m...
by rah4927
Sat Mar 04, 2017 6:44 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 3052

Re: Combi Marathon

Solution $\boxed{15}$ Suppose $a_1,...,a_n$ are the number of gems of each type. If they are arranged serially like, all $a_1$ gems of type $1$ at first, all $a_2$ gems of type $2$ next, and so on till gems of type $n$, then clearly we'll need $n$ cuts to split evenly (each cut at the middle of eac...
by rah4927
Tue Feb 28, 2017 12:59 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 3052

Re: Combi Marathon

$\text{Problem } 13$ Let $n$ be a positive integer, and let $A$ be a subset of $\{ 1,\cdots ,n\}$. An $A$-partition of $n$ into $k$ parts is a representation of n as a sum $n = a_1 + \cdots + a_k$, where the parts $a_1 , \cdots , a_k $ belong to $A$ and are not necessarily distinct. The number of di...
by rah4927
Tue Feb 28, 2017 1:01 am
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 3052

Re: Combi Marathon

$\text{Solution } 12$ Below, we distinguish between arc and coloured arc by defining an arc to be any sector of the circumference of the circle. So all coloured arcs are arcs, but not vice versa. Assume that there is no point that belongs to $n$ coloured arcs. The way we progress is by noting that i...
by rah4927
Mon Feb 27, 2017 5:26 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 3052

Re: Combi Marathon

By general consensus among most participants in this marathon, we won't be posting a solution of the above well-known problem. You can check for solutions here . $\text{Problem 11}$ Let $a_1,a_2,...,a_9$ be nine real numbers, not necessarily distinct, with average $m$. Let $A$ denote the number of t...