The Maximum Number of Sets for 12 Cards is 14
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915115433984000 |
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| author | Stevens, Justin Wilson, Duncan |
| author_facet | Stevens, Justin Wilson, Duncan |
| contents | We present a novel proof that the maximum number of sets with 4 properties for 12 cards is 14 using the geometry of the finite field F_3^4, number theory, combinatorics, and graph theory. We also present several computer algorithms for finding the maximum number of sets. In particular, we show a complete set solver that iterates over all possible board configurations. We use this method to compute the maximum number of sets with 4 properties for a small number of cards, but it is generally too inefficient. However, with this method, we compute the maximum number of sets for 3 properties for all possible numbers of cards. We also present an algorithm for constructing near-optimal maximum sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Maximum Number of Sets for 12 Cards is 14 Stevens, Justin Wilson, Duncan Combinatorics Discrete Mathematics Number Theory 05Cxx (Primary), 11Txx, 68Rxx (Secondary) G.2; G.4 We present a novel proof that the maximum number of sets with 4 properties for 12 cards is 14 using the geometry of the finite field F_3^4, number theory, combinatorics, and graph theory. We also present several computer algorithms for finding the maximum number of sets. In particular, we show a complete set solver that iterates over all possible board configurations. We use this method to compute the maximum number of sets with 4 properties for a small number of cards, but it is generally too inefficient. However, with this method, we compute the maximum number of sets for 3 properties for all possible numbers of cards. We also present an algorithm for constructing near-optimal maximum sets. |
| title | The Maximum Number of Sets for 12 Cards is 14 |
| topic | Combinatorics Discrete Mathematics Number Theory 05Cxx (Primary), 11Txx, 68Rxx (Secondary) G.2; G.4 |
| url | https://arxiv.org/abs/2501.12565 |