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Found problems: 1

2016 NIMO Problems, 3
Tags: 3 way tie
A round-robin tournament has six competititors. Each round between two players is equally likely to result in a win for a given player, a loss for that player, or a tie. The results of the tournament are \textit{nice} if for all triples of distinct players $(A, B, C)$, 1. If $A$ beat $B$ and $B$ beat $C$, then $A$ also beat $C$; 2. If $A$ and $B$ tied, then either $C$ beat both $A$ and $B$, or $C$ lost to both $A$ and $B$. The probability that the results of the tournament are $\textit{nice}$ is $p = \tfrac{m}{n}$, for coprime positive integers $m$ and $n$. Find $m$. [i]Proposed by Michael Tang[/i]