Related papers: Muddy Waters
While state-of-the-art LLMs have shown poor logical and basic mathematical reasoning, recent works try to improve their problem-solving abilities using prompting techniques. We propose giving "hints" to improve the language model's…
In this note, we give an explicit polynomial-time executable strategy for Peter Winkler's hat guessing game that gives superior results if the distribution of hats is imbalanced. While Winkler's strategy guarantees in any case that $\lfloor…
The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new…
Preferences for mixing can reveal ambiguity perception and attitude on a single event. The validity of the approach is discussed for multiple preference classes including maxmin, maxmax, variational, and smooth second-order preferences. An…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
We present a variation of the water puzzle, which is related to a simple model of marginal utility. The problem has an intriguing solution and can be extended in several directions.
Hedges allow speakers to mark utterances as provisional, whether to signal non-prototypicality or "fuzziness", to indicate a lack of commitment to an utterance, to attribute responsibility for a statement to someone else, to invite input…
A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic.…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
People reason heuristically in situations resembling inferential puzzles such as Bertrand's box paradox and the Monty Hall problem. The practical significance of that fact for economic decision making is uncertain because a departure from…
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
In this paper I investigate the problem of tagging elements of a set, and the elements of those elements, uniquely, when they admit an order, and two boundary elements are tagged. A heuristic sorting algorithm is also investigated. (Updated…
Erd\H{o}s first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in…
I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific…
A popular demonstration experiment in optics uses a round-bottom flask filled with water to project a circular rainbow on a screen with a hole through which the flask is illuminated. We show how the vessel's wall shifts the second-order and…
This article contains a selection of problems from the American Mathematics Competitions.
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
We describe in detail an advanced project devised for outstanding High School (or undergraduate) students with appropriate abilities in physical reasoning (rather than with a good standard preparation), centered around the well-known…
Artificial intelligence systems are being increasingly deployed due to their potential to increase the efficiency, scale, consistency, fairness, and accuracy of decisions. However, as many of these systems are opaque in their operation,…
Math is the backbone of any field. Still its a night mare for many. Recent survey proves that many students become dropouts from their higher education due to math courses. ICT is an enchanted word in the contemporary educational…