Related papers: 100 prisoners and a lightbulb -- looking back
A puzzle about prisoners trying to identify the color of a hat on their head leads to a version where there are k more hats than prisoners. This generalized puzzle is related to the independence number of the arrangement graph A(m, n) and…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
While many theoretical studies have revealed the strategies that could lead to and maintain cooperation in the Iterated Prisoner's Dilemma, less is known about what human participants actually do in this game and how strategies change when…
This manuscript explores the research topics and collaborative behaviour of authors in the field of the Prisoner's Dilemma using topic modeling and a graph theoretic analysis of the co-authorship network. The analysis identified five…
This is a review of topics which haunted me for the last 40 years, starting with spontaneous symmetry breaking and ending with gauge/string/space-time correspondence. While the first part of this article is mostly historical, the second…
This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…
The three years 2001 to 2003 were the golden years of solar neutrino research. In this period, scientists solved a mystery with which they had been struggling for four decades. The solution turned out to be important for both physics and…
The Prisoner's Dilemma is used to represent many real life phenomena whether from the civilized world of humans or from the wild life of the other living. Researchers working on iterated prisoner's dilemma (IPD) with limited memory…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning…
In this paper I present a mathematically novel approach to the Prisoner's Dilemma. I do so by first defining recursively a distinct action type, what I call 'universalizing', that I add to the original prisoner's dilemma. Such a modified…
The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata,…
The Light-Up puzzle, also known as the AKARI puzzle, has never been solved using modern artificial intelligence (AI) methods. Currently, the most widely used computational technique to autonomously develop solutions involve evolution theory…
This paper discusses a problem that consists of $n$ "lighthouses" which are circles with radius 1, placed around a common center, equidistant at $n$ units away from the placement center. Consecutive lighthouses are separated by the same…
We introduce the stochastic Network-Iterated Prisoner's Dilemma (NIPD) model, a network of players playing the Prisoner's Dilemma with their neighbours, each with a memory-one strategy which they constantly and locally update to improve…
Ball lightning is a very rarely observed phenomenon that makes it extremely difficult to characterize scientifically. Eye-witness accounts of ball lightning that describe many features in common have been variously recorded for centuries.…
Context: Open public data enable different stakeholders to perform analysis and uncover information from different perspectives. The identification and analysis of data from prison systems is not a trivial task. It raises the need for the…
Consider the commonly known puzzle, given $k$ glass balls, find an optimal algorithm to determine the lowest floor of a building of $n$ floors from which a thrown glass ball will break. This puzzle was originally posed in its original form…
A very brief and popular account of the time machine problem.
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…