17 papers
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…
Immensely Questionable Tests
Siyona Agarwal, Julian Bernhoft, Karam Gill +8
We study self-referential multiple-choice tests in which the answer choices are positive integers and the question asks how many answer choices are correct. These tests quickly lea…
Self-Referential Tests
Siyona Agarwal, Julian Bernhoft, Karam Gill +8
We study self-referential multiple-choice tests with the question: \emph{How many correct answer choices are there?} The answer choices are positive integers. A value is called…
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.
PRIMES STEP Experience
Slava Gerovitch, Tanya Khovanova
PRIMES STEP is a mathematical outreach program established at MIT in 2015. STEP students study advanced topics beyond the school curriculum and conduct group research projects, oft…
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…
Card Dealing Math
Eric Huang, Tanya Khovanova, Timur Kilybayev +9
Various card tricks involve under-down dealing, where alternatively one card is placed under the deck and the next card is dealt. We study how the cards need to be prepared in the…
SET! From Groups to Games
Andrey Boris Khesin, Tanya Khovanova
The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to diffe…
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…
Card Tricks and Information
Aria Chen, Tyler Cummins, Rishi De Francesco +7
Fitch Cheney's 5-card trick was introduced in 1950. In 2013, Mulcahy invented a 4-card trick in which the cards are allowed to be displayed face down. We suggest our own invention:…
My Favorite Math Jokes
Tanya Khovanova
For many years, I have been collecting math jokes and posting them on my website. I have more than 400 jokes there. In this paper, which is an extended version of my talk at the G4…
Fractal Word Search: How Deep to Delve
Klára Churá, Tanya Khovanova
We look at the puzzle \textit{In the Details} which appeared in the 2013 MIT Mystery Hunt and which gained fame as the \textit{fractal word search}. This seemingly impossible puzzl…