Related papers: New problems on old solitaire boards

In this paper we present new results regarding the periodicity of outer billiards in the hyperbolic plane around polygonal tables which are tiles in regular two-piece tilings of the hyperbolic plane.

We consider outer billiard outside regular convex polygons. We deal with the case of regular polygons with $\{3,4,5,6,10\}$ sides, and we describe the symbolic dynamics of the map and compute the complexity of the language.

We identify and study a simple combinatorial problem that is derived from submodularity issues encountered in the theory of tangles of graphs and abstract separation systems.

We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…

We define on-shell symmetries and characterize them for Lagrangian systems. The terms appearing in the variation of the Poincare'-Cartan form, which vanish because of field equations, are found to be strongly constrained if the space of…

We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…

The Bulgarian solitaire is a mathematical card game played by one person. A pack of n cards is divided into several decks (or "piles"). Each move consists of the removing of one card from each deck and collecting the removed cards to form a…

In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.

This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…

The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…

We consider a problem of shuffling a deck of cards with ordered labels. Namely we split the deck of N=k^tq cards (where t>=1 is maximal) into k equally sized stacks and then take the top card off of each stack and sort them by the order of…

This paper presents a brief review of the evidence for dark matter in the Universe on the scales of galaxies. In the interests of critically and objectively testing the dark matter paradigm on these scales, this evidence is weighed against…

We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes,…

Software for the resolution of certain kind of problems, those that rate high in the Stringent Performance Objectives adjustment factor (IFPUG scheme), can be described using a combination of game theory and autonomous systems. From this…

This study employs gamified experiments to investigate and refine the Schelling Model of Segregation, a framework that demonstrates how individual preferences can lead to systemic segregation. Using a movement selection algorithm derived…

Following up on our earlier work predicting fractionally charged supermassive gravitinos, we explain their potential relevance as novel candidates for Dark Matter and discuss possible signatures and ways to detect them.

Accurately quantifying player experience is challenging for many reasons: identifying a ground truth and building validated and reliable scales are both challenging tasks; on top of that, empirical results are often moderated by individual…