| Item type |
SIG Technical Reports(1) |
| 公開日 |
2024-03-01 |
| タイトル |
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|
タイトル |
Josephus Nim |
| タイトル |
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言語 |
en |
|
タイトル |
Josephus Nim |
| 言語 |
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|
言語 |
eng |
| 資源タイプ |
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|
資源タイプ識別子 |
http://purl.org/coar/resource_type/c_18gh |
|
資源タイプ |
technical report |
| 著者所属 |
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|
Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属 |
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Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属 |
|
|
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Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属 |
|
|
|
Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属(英) |
|
|
|
en |
|
|
Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属(英) |
|
|
|
en |
|
|
Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属(英) |
|
|
|
en |
|
|
Keimei Gakuen Elementary Junior and Senior High School |
| 著者所属(英) |
|
|
|
en |
|
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Keimei Gakuen Elementary Junior and Senior High School |
| 著者名 |
Shoei, Takahashi
Hikaru, Manabe
Ryohei, Miyadera
Aoi, Murakami
|
| 著者名(英) |
Shoei, Takahashi
Hikaru, Manabe
Ryohei, Miyadera
Aoi, Murakami
|
| 論文抄録 |
|
|
内容記述タイプ |
Other |
|
内容記述 |
In this study, we propose a variant of Nim that uses two piles. In the first pile, we have stones with a weight of a, and in the second pile, we have stones with a weight of -2a, where a is a natural number. Two players take turns to remove stones from one of the piles. The total weight of the stones to be removed should be equal to or less than half of the total weight of the stones in the pile. Therefore, if there are x stones with weight a and y stones with weight -2a, then the total weight of the stones to be removed is less than or equal to (ax - 2ay)/2. The player who removes the last stone is the winner of the game. The authors discovered that when (n, m) is the winning position of the previous player, 2m + 1 is the last remaining number in the Josephus problem, where there are n + 1 numbers, and every second number is to be removed. For any natural number s, there are similar relationships between the position at which the Grundy number is s and the n - sth removed number in the Josephus problem with n + 1 numbers. |
| 論文抄録(英) |
|
|
内容記述タイプ |
Other |
|
内容記述 |
In this study, we propose a variant of Nim that uses two piles. In the first pile, we have stones with a weight of a, and in the second pile, we have stones with a weight of -2a, where a is a natural number. Two players take turns to remove stones from one of the piles. The total weight of the stones to be removed should be equal to or less than half of the total weight of the stones in the pile. Therefore, if there are x stones with weight a and y stones with weight -2a, then the total weight of the stones to be removed is less than or equal to (ax - 2ay)/2. The player who removes the last stone is the winner of the game. The authors discovered that when (n, m) is the winning position of the previous player, 2m + 1 is the last remaining number in the Josephus problem, where there are n + 1 numbers, and every second number is to be removed. For any natural number s, there are similar relationships between the position at which the Grundy number is s and the n - sth removed number in the Josephus problem with n + 1 numbers. |
| 書誌レコードID |
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|
収録物識別子タイプ |
NCID |
|
収録物識別子 |
AA11362144 |
| 書誌情報 |
研究報告ゲーム情報学（GI）
巻 2024-GI-51,
号 9,
p. 1-6,
発行日 2024-03-01
|
| ISSN |
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|
収録物識別子タイプ |
ISSN |
|
収録物識別子 |
2188-8736 |
| Notice |
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|
SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc. |
| 出版者 |
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言語 |
ja |
|
出版者 |
情報処理学会 |
IPSJ-GI24051009.pdf (947.3 kB)
