# The Mathematician's Arm Wrestle Tournament

**Discrete Mathematics**Level 2

The Mathematician's Arm Wrestle Tournament is an arm wrestling tournament that takes place every year between the world's strongest mathematicians. It is a round-robin tournament where each competitor plays every other exactly once and each game can end in only a win or a loss for a given player.

In 2015, seven mighty mathematicians entered the tournament. The table below shows a list of possible scoresheets containing the number of wins for each competitor.

Alice | Bob | Carly | Dave | Evelyn | Frank | Greg | |

Scoresheet 1 | 5 | 2 | 1 | 0 | 2 | 5 | 6 |

Scoresheet 2 | 5 | 4 | 3 | 3 | 3 | 2 | 2 |

Scoresheet 3 | 3 | 3 | 3 | 3 | 3 | 0 | 6 |

Scoresheet 4 | 5 | 4 | 1 | 1 | 4 | 0 | 6 |

Which of the score sheets reflects possible scores for that year?