Number of ways that a football league can complete with all teams having the same number of points
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912282031685632 |
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| author | Jehn, Rüdiger Habermann, Kester Lavrov, Misha |
| author_facet | Jehn, Rüdiger Habermann, Kester Lavrov, Misha |
| contents | When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat. Hence we have $3^M$ possible outcomes. In this paper the number of ways is determined that a football league can complete with all teams having the same number of points. An algorithm that works until $n=8$ is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Number of ways that a football league can complete with all teams having the same number of points Jehn, Rüdiger Habermann, Kester Lavrov, Misha General Mathematics 05C30 When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat. Hence we have $3^M$ possible outcomes. In this paper the number of ways is determined that a football league can complete with all teams having the same number of points. An algorithm that works until $n=8$ is presented. |
| title | Number of ways that a football league can complete with all teams having the same number of points |
| topic | General Mathematics 05C30 |
| url | https://arxiv.org/abs/2503.14509 |