Related papers: Chocolate Numbers
At some places (see the references) Martin Erickson describes a certain game: "Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an n x n grid. The first player (if any) to occupy four cells…
We consider a card guessing game with complete feedback. A ordered deck of n cards labeled 1 up to n is riffle-shuffled exactly one time. Then, the goal of the game is to maximize the number of correct guesses of the cards, where one after…
In 2002, Cookie Monster appeared in The Inquisitive Problem Solver. The hungry monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of…
Gauss proposed the problem of how to enumerate the number of solutions for placing $N$ queens on an $N\times N$ chess board, so no two queens attack each other. The N-queen problem is a classic problem in combinatorics. We describe a…
We modify Wythoff's game by allowing an additional move, which we call a "split", and show how the $P$-positions are coded by the Tribonacci word. We analyze the table of letter positions of arbitrary $k$-bonacci words and find a…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is shelf-shuffled exactly one time. One after the other a single card is drawn from the shuffled deck. The guesser makes has guess…
We give a new proof that any candy-passing game on a graph G with at least 4|E(G)|-|V(G)| candies stabilizes. (This result was first proven in arXiv:0807.4450.) Unlike the prior literature on candy-passing games, we use methods from the…
Consider n straight line cuts of a circular pizza made so as to maximize the number of pieces. We investigate how fair such a maximal division may be and how many slices are obtained if the cuts are successfully made with a certain…
We consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the…
We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three…
We study the $(p,q)$-Maker Breaker Crossing game introduced by Day and Falgas Ravry in 'Maker-Breaker percolation games I: crossing grids'. The game described in their paper involves two players Maker and Breaker who take turns claiming p…
Assume you have a pizza consisting of four ingredients (e.g., bread, tomatoes, cheese and olives) that you want to share with your friend. You want to do this fairly, meaning that you and your friend should get the same amount of each…
Given two players alternately picking pieces of a pizza sliced by radial cuts, in such a way that after the first piece is taken every subsequent chosen piece is adjacent to some previously taken piece, we provide a strategy for the…
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…
The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to…
The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In…
Graph pebbling is a game played on a connected graph G. A player purchases pebbles at a dollar a piece, and hands them to an adversary who distributes them among the vertices of G (called a configuration) and chooses a target vertex r. The…
We undertake the first study of the candy-passing game on arbitrary connected graphs. We obtain a general stabilization result which encompasses the first author's results (arXiv:0709.2156) for candy-passing games on n-cycles with at least…
This work is concerned with the study of the Game of Graph Nim -- a class of two-player combinatorial games -- on graphs with $4$ edges. To each edge of such a graph is assigned a positive-integer-valued edge-weight, and during each round…
In this paper we study queen's graphs, which encode the moves by a queen on an $n\times m$ chess board, through the lens of chip-firing games. We prove that their gonality is equal to $nm$ minus the independence number of the graph, and…