13 papers
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…
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…