Related papers: Monty Hall problem revisited once more
The enigmatic open clusters serve as a constant reminder of the mysteries of the universe, helping to confront astronomical theories. Unknown to many, these clusters often possess tails with inappropriate labels, serving as the tell-tale…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
There exists "a square problem": in a unit square is there a point with four rational distances to the vertices? This problem is still regarded as unproved. Yang showed proofs for several special cases of the square problem. By the…
We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
We define a countable family of sequences of points in the unit square: the {\it $LS$-sequences of points \`a la Halton}. They reveal a very strange and interesting behaviour, as well as resonance phenomena, for which we have not found an…
We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
In this paper we consider the Hamilton cycle problem in the rectangular meshes with at most two faulty nodes.We prove that this problem is solvable in polynomial time with a corresponding algorithm. We provided an entirely new approach to…
Problems solved? Pulsar research must be considered - 35 years after the detection of pulsars - a mature science, where the basic questions have been raised and discussed. One would hope that many if not all generic and important problems…
We give an historical account, including recent progress, on some problems of Erd\H os in number theory.
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…
We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global…
This paper intends to survey the vast literature devoted to a problem posed by Wilf in 1978 which, despite the attention it attracted, remains unsolved. As it frequently happens with combinatorial problems, many researchers who got involved…
The primary objective of this note is to revisit the two envelope problem and propose a simple resolution. It is argued that the paradox arises from the ambiguity associated with the money content $x of the chosen envelope. When X=x is…
We discuss the history of attempts to solve the Pell equation using certain auxiliary equations that correspond, in modern terminology, to a second 2-descent.
Some Open Problems Concerning Orthogonal Polynomials.