Related papers: The Magnetic Tower of Hanoi
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
Lomonaco and Kauffman developed a knot mosaic system to introduce a precise and workable definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an $m \times n$…
A minimal perfect hash function (MPHF) maps a set of n keys to unique positions {1, ..., n}. Representing an MPHF requires at least 1.44 bits per key. ShockHash is a technique to construct an MPHF and requires just slightly more space. It…
A picture-hanging puzzle is the task of hanging a framed picture with a wire around a set of nails in such a way that it can remain hanging on certain specified sets of nails, but will fall if any more are removed. The classical brain…
This work presents the publicly available moving-mesh magnetohydrodynamics code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach number. DISCO employs a moving-mesh…
Frustrated magnetism continues to attract significant attention due to its potential to host novel quantum many-body phenomena and associated exotic excitations that transcend existing paradigms. Herein, we present our reply to the comment…
Mosaic tiles were first introduced by Lomonaco and Kauffman in 2008 to describe quantum knots, and have since been studied for their own right. Using a modified set of tiles, front projections of Legendrian knots can be built from mosaics…
This puzzle, often called the "Reverse the Triangle Puzzle," appears regularly in puzzle books. Four rows consisting of 1 coin in row 1, 2 coins in row 2, 3 coins in row 3, and 4 coins in row 4 form the shape of a triangle. What is the…
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
Lomonaco and Kauffman introduced a knot mosaic system to give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This paper is inspired by an open question about the knot mosaic…
In this paper, we present the clockwise-algorithm that solves the extension in $k$-dimensions of the infamous nine-dot problem, the well-known two-dimensional thinking outside the box puzzle. We describe a general strategy that…
Retraction note: After posting the manuscript on arXiv, we were informed by Erik Jan van Leeuwen that both results were known and they appeared in his thesis[vL09]. A PTAS for MDS is at Theorem 6.3.21 on page 79 and A PTAS for MCDS is at…
The Knight's Tour problem consists of finding a Hamiltonian path for the knight on a given set of points so that the knight can visit exactly once every vertex of the mentioned set. In the present paper, we provide a $5$-dimensional…
"Eye-Witless", "Haisu" and "Oriental House" are genres of logic puzzles invented by William Hu, and "Detour" is a genre of logic puzzle invented by online user Guowen Zhang. Each of these puzzles revolves around constructing a path or loop…
A deck of $n$ cards is shuffled by repeatedly moving the top card to one of the bottom $k_n$ positions uniformly at random. We give upper and lower bounds on the total variation mixing time for this shuffle as $k_n$ ranges from a constant…
The Cookie Monster Problem supposes that the Cookie 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 cookies from each of those…
The cryptographic protocol based on topological knot theory,recently proposed by the authors, is improved for what concerns the efficiency of the encoding of knot diagrams and its error robustness. The standard Dowker-Thistlethwaite code,…
We discuss two approaches to a recent question of Loh: must a 3-colored transitive tournament on $N$ vertices have a 1-color-\emph{avoiding} path of vertex-length at least $N^{2/3}$? This question generalizes the Erd\H{o}s--Szekeres theorem…
We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get…
Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the column at position (0,0). For non-negative integers u,w such…