The transversal game
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912463326281728 |
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| author | Ranđelović, Žarko |
| author_facet | Ranđelović, Žarko |
| contents | Two players take turns claiming empty cells from an $n\times n$ grid. The first player (if any) to occupy a transversal (a set of $ n $ cells having no two cells in the same row or column) is the winner. What is the outcome of the game given optimal play? Our aim in this paper is to show that for $n\ge 4$ the first player has a winning strategy. This answers a question of Erickson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The transversal game Ranđelović, Žarko Combinatorics 91A05 G.2.1 Two players take turns claiming empty cells from an $n\times n$ grid. The first player (if any) to occupy a transversal (a set of $ n $ cells having no two cells in the same row or column) is the winner. What is the outcome of the game given optimal play? Our aim in this paper is to show that for $n\ge 4$ the first player has a winning strategy. This answers a question of Erickson. |
| title | The transversal game |
| topic | Combinatorics 91A05 G.2.1 |
| url | https://arxiv.org/abs/2401.16768 |