6 papers · 1 filter
Purely Periodic Three-move Subtraction Games
Hikaru Manabe
We determine the full Sprague-Grundy sequence and its least period for a class of three-move subtraction games whose sequences are periodic from the start. Write the move set as $S…
A Subtraction Nim with a Pass
Urban Larsson, Hikaru Manabe, Ryohei Miyadera
We consider a subtraction Nim with subtraction set {s_1,s_2,s_3={2,4n,4n+2}, where n is a positive integer such that n >= 3. We do not treat the case that n=1 or n=2 in this articl…
Additive Subtraction Games
Urban Larsson, Hikaru Manabe
We determine the full nim-value structure of additive subtraction games in the {\em primitive quadratic} regime. The problem appears in Winning Ways by Berlekamp et al. in 1982; it…
Additive sink subtraction
Anjali Bhagat, Urban Larsson, Hikaru Manabe +1
Subtraction games are a classical topic in Combinatorial Game Theory. A result of Golomb~(1966) shows that every subtraction game with a finite move set has an eventually periodic…
Digraph Yama Nim
Hiyu Inoue, Shun-ichi Kimura, Hikaru Manabe +3
{\sc Yama Nim} is a variant of two piles {\sc Nim}. In this ruleset, the player chosses one of the piles and removes at least two tokens from the pile. In the same move, the player…
An Amalgamation Nim with Restriction
Hikaru Manabe
In an amalgamation Nim, players are allowed to use a move from the traditional form of Nim or to amalgamate two piles when they are not empty. No formula that describes the set of…