Related papers: It's Common Knowledge
What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…
Sudoku is a popular combinatorial puzzle. A new method of solving Sudoku is presented, which involves formulating a puzzle as a special type of transportation problem. This model allows one to solve puzzles with more than one solution,…
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying mathematics and describe how they are naturally associated…
We discuss a generalization of logic puzzles in which truth-tellers and liars are allowed to deviate from their pattern in case of one particular question: "Are you guilty?"
New cases of the multiplicity conjecture are considered.
We revisit a recent puzzle about common knowledge, the ``sailboat" case (Lederman, 2018), and argue that Lewisian common knowledge allows us to reconcile the pre-theoretical intuition that certain facts are ``public" in such situations,…
The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for…
In this paper we present many congruences for several Ap\'ery-like sequences.
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
This is an update of my problem list.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
This is a very basic introduction to some notions related to logic and complexity.
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical…
A sequence of positive integers is introduced, that is proved to simultaneously solve an infinite family of related puzzles, one of which was recently featured on the popular YouTube sudoku channel \emph{Cracking the Cryptic}.
When presented with information of any type, from music to language to mathematics, the human mind subconsciously arranges it into a network. A network puts pieces of information like musical notes, syllables or mathematical concepts into…
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…