Related papers: Conway's Wizards

We introduce a very simple solitaire game, named Stanley Solitaire, in honor of Richard Stanley, and prove an explicit closed-form formula for the number of ways of playing it. Alas, the only proof that we know is via a deep theorem of…

The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.

I discuss puzzles that require thinking outside the box. I also discuss the box inside of which many people think.

In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.

In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.

The Hummer Principle was born from the mind of Bob Hummer in 1946, which consists of performing card shuffles with an even number of cards while leaving some properties of the deck intact. In this document, we will present a generalization…

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram `exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of diagrams we call…

We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is…

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

We show how degeneracies, accidental or otherwise, can obscure some interesting physics. We further show how one can get around this problem.

A short history of prisms from Lucius Anneus Seneca to George Ravenscroft.

In the stories of Carnacki, created by the English writer William H. Hodgson and written between 1910 and 1912, we find an interesting mixture of science and fantasy. In spite of the fact that Carnacki is a ghost finder, who investigates in…

We review the state of the art in the problem of counting the number open knight tours, since the publication in internet of a computation of this quantity.

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…

Peg solitaire is classically a one-player game played on a grid board containing pegs. The goal of the game is to have a single peg remaining on the board by sequentially jumping with a peg over an adjacent peg onto an empty cell while…

A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have.…

We discuss the classical, and forgotten, notion of perpetuants. We give a proof of the Theorem of Stroh computing their dimensions, and exhibit a basis of perpetuants, thus closing an old line of investigation.