Related papers: A note on the problem of prisoners and hats

The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…

The problems of enumerating lattice walks, with an arbitrary finite set of allowed steps, both in one and two dimensions, where one must always stay in the non-negative half-line and quarter-plane respectively, are used, as case studies, to…

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

This paper is the first in series of four papers that present an analytical approach to war using game theory. We try to explore why is it that "true peace" can't be achieved and all or any efforts we make towards that goal will have huge…

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…

The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are…

We emphasize the dominance in the Monty Hall problem, both in the classical scenario and its multi-door generalization. This is used to show optimality of the class of always-switching strategies for nonuniform allocation of the prize and…

We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which…

Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population…

In this note we prove a weighted version of the Khintchine inequalities.

We theoretically study the effect of a third person enforcement on a one-shot prisoner's dilemma game played by two persons, with whom the third person plays repeated prisoner's dilemma games. We find that the possibility of the third…

We study the binary Goldbach problem with arithmetic weights attached to one of the variables.

In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…

This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…

A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…

The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…

This note describes a SAT encoding for the $n$-fractions puzzle which is problem 041 of the CSPLib. Using a SAT solver we obtain a solution for two of the six remaining open instances of this problem.

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

This is perhaps a philosophical question rather than a mathematical one, we do not expect to give a full answer, even though we hope to clarify some ideas. In addition, we would like to provide a new perspective on the subject. We will find…

We discuss coin-weighing problems with a new type of coin: a chameleon. A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently. We consider a mix of $N$ coins that include…