Related papers: A note on the problem of prisoners and hats
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.
Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists,…
In this paper we provide an application to the Neumann problem of a recent three critical points theorem.
We examine what integers are representable as sums of three cubes. We also provide formulas for the number of representations of $x^3+y^3+z^3=n$ under the condition $x+y+z=t$. Also we show how the problem of three cubes is related to…
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…
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.
In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel…
A formal axiomatic mathematical framework for Boolos' Hardest Logic Puzzle Ever is presented and two theorems about its solvability are proved. By strictly following Boolos' instructions (in particular, the requirement that all gods are…
We use replicator dynamics to study an iterated prisoners' dilemma game with memory. In this study, we investigate the characteristics of all 32 possible strategies with a single-step memory by observing the results when each strategy…
Using the representation introduced in our another paper\cite{frame}, the well-known Quantum Prisoner's Dilemma proposed in \cite{jens}, is reexpressed and calculated. By this example and the works in \cite{frame} on classical games and…
We consider a bandit problem which involves sequential sampling from two populations (arms). Each arm produces a noisy reward realization which depends on an observable random covariate. The goal is to maximize cumulative expected reward.…
We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…