Related papers: Monty Hall problem revisited once more

100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums…

The "interior goat problem" is a numerical puzzle which has haunted mathematicians for nearly three centuries. Closed-form solutions have only been found for the two-dimensional case, and although approximations have been established for…

We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified "mathematical response". We then consider and rebut two prominent critiques of the…

This is an update of my problem list.

This paper attempts to explain the mystery behind an 18th elephant that appears in many popular legends involving the division of a herd of 17 elephants into groups in the ratio 1/2:1/3:1/9.

These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one…

The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…

ApSimon's Mints problem is a very difficult and often misunderstood counterfeit-coin puzzle. I explain the problem and suggest ways to approach it, while giving several fun exercises for the reader.

Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…

This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…

The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer…

The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…

We clarify and generalize the ant on a rubber rope paradox, which is a mathematical puzzle with a solution that appears counterintuitive. In this paper, we show that the ant can still reach the end of the rope even if we consider the step…

In the paper, using the language of spin-half particles, Hardy's paradox is examined within different semantics: a partial one, a many-valued one, and one defined as a set of weak values of projection operators. As it is shown in this…

We reinterpret the distribution of the Hall potential in the Hall bar-with-a-hole that has been found and interpreted by Mani and Klitzing [Appl. Phys. Lett., 64 1262 (1994)]. Our reinterpretation explains all the "paradoxes" without…

Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970's, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have…

The identification of a solution to the dark matter problem has many arrows to its bow: if dark matter is a new elementary particle, both laboratory experiments and astrophysics can bring relevant and complementary pieces of information,…

NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…

In this piece, we examine one variant of the infamous 15 Tile Puzzle and develop a mathematical backing behind why it is unsolvable. Using concepts of permutations, bijectivity, and cycle transpositions, we not only prove how to model this…

Conway's 99-graph problem is the second problem amongst the five 1000\$ 2017 open problems set. Four out of the five remain unsolved to this day, including the 99-graph problem. In this paper we quote Conway's definition of the problem and…