Related papers: Hat Puzzles
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.
These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published in the London Mathematics Society Lecture Notes Series. It gives a…
In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…
Riddles based on simple puns can be classified according to the patterns of word, syllable or phrase similarity they depend upon. We have devised a formal model of the semantic and syntactic regularities underlying some of the simpler types…
We propose a funny representation of SAT. While the primary interest is to present propositional satisfiability in a playful way for pedagogical purposes, it could also inspire new search heuristics.
Several different "hat games" have recently received a fair amount of attention. Typically, in a hat game, one or more players are required to correctly guess their hat colour when given some information about other players' hat colours.…
The prisoners and hats puzzle, or simply the hat puzzle, is a family of games in which a group of prisoners are each assigned a colored hat and are asked to guess the color of their own hat. Various versions of the puzzle arise depending on…
These are informal notes written in 2007 that outline the local and global quantum Langlands program. (I decided to make them public in view of the revived interest in the subject.)
The goal of this article is to introduce some beautiful known riddles in intuitive topology; hoping to make at least some fun for the reader.
Humor is a magnetic component in everyday human interactions and communications. Computationally modeling humor enables NLP systems to entertain and engage with users. We investigate the effectiveness of prompting, a new transfer learning…
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…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
This is a very short paper that briefly discusses some of the tasks that NLG systems perform. It is of no research interest, but I have occasionally found it useful as a way of introducing NLG to potential project collaborators who know…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
We revisit the cocked hat -- an old problem from navigation -- and examine under what conditions its old solution is valid.
In the 2013 Advent calender of the Berlin Mathematics Research Center MATH+, Gerhard Woeginger presents a novel hat problem with an uncommon initial announcement. Although the information given is insufficient for the hat bearers to learn…
This paper introduces a novel method, referred to as "hashing", which involves masking potentially bias-inducing words in large language models (LLMs) with hash-like meaningless identifiers to reduce cognitive biases and reliance on…