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A Variant of Game of Sliding Coins
Ryohei Miyadera, Hikaru Manabe, Unchon Lee
Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered . Two players…
On the Sprague-Grundy values of games with a pass
Hikaru Manabe, Ryohei Miyadera, Koki Suetsugu
In this paper, we consider two-player impartial games with a pass-move. A disjunctive compound of games is a position in which, on each turn, the current player chooses one of the…
Maximum Nim and Josephus Problem algorithm
Shoei Takahashi, Hikaru Manabe, Ryohei Miyadera
In this study, we study a Josephus problem algorithm. Let be positive integers and , where $ \left\lfloor \ \ \right\rfl…
Maximum Nim and Josephus Problem
Shoei Takahashi, Hikaru Manabe, Ryohei Miyadera
In this study, we study the relation between Grundy numbers of a Maximum Nim and Josephus problem. Let f(x) = floor(x/k), where floor( ) is the floor function and k is a positive i…
Josephus Nim
Shoei Takahashi, Hikaru Manabe, Aoi Murakami +1
Here, we present a variant of Nim with two piles. In the first pile, we have stones with a weight of 1, and in the second pile, we have stones with a weight of -2. Two Players take…
Games of Nim with Dynamic Restrictions
Keita Mizugaki, Shoei Takahashi, Hikaru Manabe +2
The authors present formulas for the previous player's winning positions of two variants of restricted Nim. In both of these two games, there is one pile of stones, and in the firs…
A complete solution for the partisan chocolate game
Tomoaki Abuku, Hikaru Manabe, Richard J. Nowakowski +2
The class of Poset Take-Away games includes many interesting and difficult games. Playing on an -dimensional positive quadrant (the origin being the bottom of the poset) gives r…
Impartial and Partizan Restricted Chocolate Bar Games
Ryohei Miyadera, Shoei Takahashi, Aoi Murakami +2
In this paper, we consider impartial and partizan restricted chocolate bar games. In impartial restricted chocolate bar games, players cut a chocolate bar into two pieces along any…
Multi-Dimensional Chocolate and Nim with a Pass
Ryohei Miyadera, Hikaru Manabe
Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the c…
Previous Player's Positions of Impartial Three-Dimensional Chocolate-Bar Games
Ryohei Miyadera, Hikaru Manabe, Shunsuke Nakamura
In this study, we investigate three-dimensional chocolate bar games, which are variants of the game of Chomp. A three-dimensional chocolate bar is a three-dimensional array of cube…
Restricted Nim with a Pass
Ryohei Miyadera, Hikaru Manabe
This paper presents a study of restricted Nim with a pass. In the restricted Nim considered in this study, two players take turns and remove stones from the piles. In each turn, wh…
Wythoff's Game with a Pass
Ryohei Miyadera, Hikaru Manabe, Masanori Fukui
This paper describes Wythoff's game with a pass, which is a variant of the classical Wythoff's game. The classical form is played with two piles of stones, from which two players t…