Related papers: Muddy Waters
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
N players are randomly fitted with a colored hat (q different colors). All players guess simultaneously the color of their own hat observing only the hat colors of the other N-1 players. The team wins if all players guess right. No…
Contemporary approaches frame the color constancy problem as learning camera specific illuminant mappings. While high accuracy can be achieved on camera specific data, these models depend on camera spectral sensitivity and typically exhibit…
Distributional data tells us that a man can swallow candy, but not that a man can swallow a paintball, since this is never attested. However both are physically plausible events. This paper introduces the task of semantic plausibility:…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
The enhancement of mathematical capabilities in large language models (LLMs) fosters new developments in mathematics education within primary and secondary schools, particularly as they relate to intelligent tutoring systems. However, LLMs…
The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one…
This paper studies Ebert's hat problem with four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies…
Math Word Problem (MWP) solving is a critical task in natural language processing, has garnered significant research interest in recent years. Various recent studies heavily rely on Seq2Seq models and their extensions (e.g., Seq2Tree and…
The difficulty of multiple-choice questions (MCQs) is a crucial factor for educational assessments. Predicting MCQ difficulty is challenging since it requires understanding both the complexity of reaching the correct option and the…
This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning…
An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a…
The following general variant of deterministic Hats game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the $k$-th sage can have hats of one of $h(k)$ colors. Each sage tries to guess the color of his own…
We present the general Hardy-like quantum pigeonhole paradoxes for \textit{n}-particle states, and find that each of such paradoxes can be simply associated to an un-colorable solution of a specific vertex-coloring problem induced from the…
We study a discrete diffusion process introduced in some combinatorial games called FLOODIT and MADVIRUS that can be played online and whose computational complexity has been recently studied by Arthur et al (FUN'2010). The flooding…
This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls…
We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set…
Many proposed methods for explaining machine learning predictions are in fact challenging to understand for nontechnical consumers. This paper builds upon an alternative consumer-driven approach called TED that asks for explanations to be…
Epistemic protocols represents a current field of interest, with numerous approaches still being studied. In this paper we formalize parallel sessions of the The Muddy Children Puzzle using Public Observation Logic, a system that allows…
Many prediction tasks contain uncertainty. In some cases, uncertainty is inherent in the task itself. In future prediction, for example, many distinct outcomes are equally valid. In other cases, uncertainty arises from the way data is…