Statement

A group of N people decided to play a rock paper scissors tournament, but they realised that everyone was too predictable. Therefore, they decided to make it more interesting by playing rock paper scissors lizard spock, due to language difficulties they played the game with the numbers 0, 1, 2, 3, 4 instead of names. Similarly to the original game, the winner can be determined for any pair of different numbers. Let x and y be two different numbers from 0 to 4, then x beats y if y = x + 1 \mod 5 or y = x + 2 \mod 5. It is easy to see that if x≠ y then either x or y is the winner. The game proceeds as follows: each player i chooses a number x_i from 0 to 4. Then for each pair of different players i, j, they decide who the winner is as follows: (1) If x_i = x_j, then they flip a coin to determine the winner. (In other words, either one of them can be the winner.) (2) Otherwise the winner is determined by the game's rules based on x_i and x_j...