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{\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 adds one token to the other pile. We show the winning…

We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the…

Combinatorics · Mathematics 2009-04-06 Elise Janvresse , Steve Kalikow , Thierry De La Rue

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…

Combinatorics · Mathematics 2026-04-17 Antoine Dailly , Eric Duchene , Urban Larsson , Gabrielle Paris

We study impartial take away games on 2 unordered piles of finite nonnegative numbers of tokens $(x,y)$. Two players alternate in removing at least one and at most all tokens from the respective piles, according to certain rules, and the…

Combinatorics · Mathematics 2012-06-21 Urban Larsson

Given $n$ piles of tokens and a positive integer $k \leq n$, the game Nim$^1_{n, =k}$ of exact slow $k$-Nim is played as follows. Two players move alternately. In each move, a player chooses exactly $k$ non-empty piles and removes one token…

Combinatorics · Mathematics 2021-02-09 Nikolay Chikin , Vladimir Gurvich , Konstantin Knop , Mike Paterson , Michael Vyalyi

We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and…

History and Overview · Mathematics 2014-07-08 Tanya Khovanova , Joshua Xiong

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question…

Combinatorics · Mathematics 2007-05-23 Uri Blass , Aviezri S. Fraenkel , Romina Guelman

Given $n$ piles of tokens and a positive integer $k \leq n$, we study the following two impartial combinatorial games Nim$^1_{n, \leq k}$ and Nim$^1_{n, =k}$. In the first (resp. second) game, a player, by one move, chooses at least $1$ and…

Combinatorics · Mathematics 2015-08-25 Vladimir Gurvich , Nhan Bao Ho

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…

Computer Science and Game Theory · Computer Science 2011-11-22 Adam O. Kalinich

The class of Poset Take-Away games includes many interesting and difficult games. Playing on an $n$-dimensional positive quadrant (the origin being the bottom of the poset) gives rise to nim, wythoff's nim and chomp. These are impartial…

Combinatorics · Mathematics 2023-10-23 Tomoaki Abuku , Hikaru Manabe , Richard J. Nowakowski , Carlos P. Santos , Koki Suetsugu

We present a new family of Nim games where the rules depend on a given `coloring' of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We…

Combinatorics · Mathematics 2011-08-09 Urban Larsson

We prove that playing Candy Crush to achieve a given score in a fixed number of swaps is NP-hard.

Computational Complexity · Computer Science 2014-03-11 Toby Walsh

The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these…

Combinatorics · Mathematics 2010-10-08 Lindsay Erickson

We present and analyze PackIt!, a turn-based game consisting of packing rectangles on an $n \times n$ grid. PackIt! can be easily played on paper, either as a competitive two-player game or in \emph{solitaire} fashion. On the $t$-th turn, a…

Combinatorics · Mathematics 2024-05-17 Thomas Garrison , Marijn J. H. Heule , Bernardo Subercaseaux

The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes…

Combinatorics · Mathematics 2010-10-29 Urban Larsson

We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…

Combinatorics · Mathematics 2021-04-20 Stephanie McCoy , Nándor Sieben

The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim, Restricted Nim, which restricts the number of stones a player may remove from a heap in terms of the size of the…

Combinatorics · Mathematics 2007-05-23 Lionel Levine

We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…

Combinatorics · Mathematics 2019-03-11 Ho-Hon Leung , Thotsaporn "Aek'' Thanatipanonda

Children, sitting in a circle, each have a nonnegative number of candies in front of them. A whistle is blown and each child with more than one candy passes one candy to the left and one to the right. The sharing process is repeated until a…

Combinatorics · Mathematics 2015-12-14 Grant Cairns

The ordinary game of Nim has a long history and is well-known in the area of combinatorial game theory. The solution to the ordinary game of Nim has been known for many years and lends itself to numerous other solutions to combinatorial…

Combinatorics · Mathematics 2012-08-29 Lindsay Erickson , Warren Shreve