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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.00246 |
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| _version_ | 1866915421319331840 |
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| author | Rammenstein, Tim |
| author_facet | Rammenstein, Tim |
| contents | We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility condition. We introduce a generalized version of the original game, which depends on two parameters: the size of the initial number set and a fixed divisor. For both players, we identify a broad range of game variants in which they can force a win. In particular, we show that for even-sized sets, the second player to move can always win, while for many odd-sized cases, the first player to move has a winning strategy. A web implementation of the game demonstrates some of our results in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Existence of Optimal Strategies in a Combinatorial Game Rammenstein, Tim Combinatorics We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility condition. We introduce a generalized version of the original game, which depends on two parameters: the size of the initial number set and a fixed divisor. For both players, we identify a broad range of game variants in which they can force a win. In particular, we show that for even-sized sets, the second player to move can always win, while for many odd-sized cases, the first player to move has a winning strategy. A web implementation of the game demonstrates some of our results in practice. |
| title | On the Existence of Optimal Strategies in a Combinatorial Game |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.00246 |