9 papers · 1 filter
Fair Duels after a False Start
Tanya Khovanova, Tejo Madhavarapu
In the fair dueling game, two players take turns shooting at each other, with the turn order defined by the following fairness criterion: the next shot is assigned to the player wh…
From a Voucher Puzzle to Extremal Sums of Adjacent Products
Chris Chen, Vivian Chen, Ray Cui +10
Motivated by a self-referential puzzle, we study sequences of voucher price tags in which each choice multiplies the cost of the following one. We connect the puzzle setting to cla…
Minimal 3-regular Penny Graph
Alexander Karabegov, Tanya Khovanova
We prove that a 3-regular penny graph has at least 16 vertices and show that such a graph with 16 vertices exists.
Chip-firing on the Lattice of Nonnegative Integer Points
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we stud…
Labeled Chip-Firing on Directed -ary Trees and Where Chips Land
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game played on a graph, in which chips are placed and dispersed on the vertices until a stable configuration is achieved. We study a chip-firing vari…
Permutation-based Strategies for Labeled Chip-Firing on -ary Trees
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game on a graph, in which chips are placed and dispersed among its vertices until a stable configuration is achieved. We specifically study a chip-fi…
Chip-Firing on Infinite -ary Trees
Dillan Agrawal, Selena Ge, Jate Greene +8
We use an infinite -ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with chips at the root. We describe the stable…
Chip Firing on Directed -ary Trees
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an…
On Chip-Firing on Undirected Binary Trees
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop t…