Related papers: Conway's Wizards

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].

We establish Conway's thrackle conjecture in the case of spherical thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.

Sprouts is a two-player pencil-and-paper game invented by John Conway and Michael Paterson in 1967. In the game, the players take turns in joining dots by curves according to simple rules, until one player cannot make a move. The game of…

We recall a combinatorial derivation of the functions generating probability of winnings for each of many participants of the Penney's game and show a generalization of the Conway's formula to this case.

We investigate the complexity of a puzzle that turns out to be NL-complete.

In his celebrated book "On Number and Games" (Academic Press, New-York, 1976), J.H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node-Kayles game on paths. For usual disjunctive compound,…

We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.

This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.

The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.

We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls,…

John Conway's Circle Theorem is a gem of plane geometry. The six points formed by continuing the sides of a triangle beyond every vertex by the length of its opposite side, are concyclic. The theorem has attracted several proofs. We present…

I introduce, solve and generalize a new coin puzzle that involves parallel weighings.

This is a brief introduction to the geometric aspects of aperiodic tiling and the collaboration of John Conway and the author in the decade 1990-2000.

We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game. In contrast, the similar problems of determining whether…

Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.

Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.

John Conway proved that every audioactive sequence (a.k.a. look-and-say) decays into a compound of 94~elements, a statement he termed the cosmological theorem. The underlying audioactive process can be modeled by a finite-state machine,…

We prove a recent conjecture of Sean A. Irvine about a nonlinear recurrence, using mechanized guessing and verification. The theorem-prover Walnut plays a large role in the proof.

We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…