Related papers: Conway's Wizards
An operation of joining coset diagrams for a given group, introduced by Higman and developed by Conder in connection with Hurwitz groups, is reinterpreted and generalised as a connected sum operation on dessins d'enfants of a given type. A…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
This paper presents a solution to the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight or a spy. Knights always tell the truth, while spies may…
About the relation between a counterexample in the theory of numbers constructible by ruler and compass, due to Ian Stewart, and Alhazen's problem concerning the circular mirror.
In this paper, we introduce the concept of triad. Using this notion, we study, revisit, discover and rediscover some basic properties of ludics from a very general point of view.
The author considers a class of mechatronic puzzles falling in the mixed-reality category, present examples of such devices, and propose a way to categorize them. Close relationships of such devices with the Tangible User Interface are…
Jigsaw puzzle solving requires the rearrangement of unordered pieces into their original pose in order to reconstruct a coherent whole, often an image, and is known to be an intractable problem. While the possible impact of automatic puzzle…
"The hardest logic puzzle ever" presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available…
A slightly(!!!) philosophical article which looks at some interesting overlaps between some fine mathematical brains and a celestial mechanics legend from Japan.
Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to…
Benjamin Franklin constructed three squares which have amazing properties, and his method of construction has been a mystery to date. In this article, we divulge his secret and show how to construct such squares for any order.
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
The goal of this article is to introduce some beautiful known riddles in intuitive topology; hoping to make at least some fun for the reader.
J.P. Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the other is determined by the…
A table of the families of alternating knots formed by conways is presented. The Conway's function is shown with the use of linear algebra in terms of natural numbers, called conways, that represent the number of crossings along a…
A formula concerning counting of paths was conjectured by Herzog and Conca few years ago. Recently, Krattenthaler and Prohaska gave an affirmative answer to this conjecture. In this paper we generalize this formula.
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
In this paper the circulant Hadamard conjecture is proved.
We motivate and explain the system introduced by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used…
In this article the discovery of the Jones Polynomial will be discussed, emphasizing the way in which it illustrated the remarkable unity between distinct parts of Mathematics, each with its own language, but initially without a dictionary.