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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2112.04965 |
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| _version_ | 1866929258689986560 |
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| author | Korsky, Samuel |
| author_facet | Korsky, Samuel |
| contents | We consider a game in which a blindfolded player attempts to set $n$ counters lying on the vertices of a rotating regular $n$-gon table simultaneously to $0$. When the counters count$\pmod{m}$ we simplify the argument of Bar Yehuda, Etzion, and Moran (1993) showing that the player can win if and only if $n = 1$, $m = 1$, or $(n, m) = (p^a, p^b)$ for some prime $p$ and $a, b \in \mathbb{N}$. We broadly generalize the result to the setting where the counters can be permuted by any element of a subset of the symmetric group $S \subseteq S_n$, with the original formulation corresponding to $S = \mathbb{Z}_n$ (rotations of the table). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_04965 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Permutations of counters on a table Korsky, Samuel Combinatorics We consider a game in which a blindfolded player attempts to set $n$ counters lying on the vertices of a rotating regular $n$-gon table simultaneously to $0$. When the counters count$\pmod{m}$ we simplify the argument of Bar Yehuda, Etzion, and Moran (1993) showing that the player can win if and only if $n = 1$, $m = 1$, or $(n, m) = (p^a, p^b)$ for some prime $p$ and $a, b \in \mathbb{N}$. We broadly generalize the result to the setting where the counters can be permuted by any element of a subset of the symmetric group $S \subseteq S_n$, with the original formulation corresponding to $S = \mathbb{Z}_n$ (rotations of the table). |
| title | Permutations of counters on a table |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2112.04965 |