Related papers: Murder at the Asylum
This report examines a novel risk associated with current (and projected) AI tools. Making effective decisions about future actions requires us to reason under uncertainty (RUU), and doing so is essential to many critical real world…
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}.
In this missive, the author goes about ruining an online word guessing game called Wordle, by generally trying to mathify the whole thing. On the other hand, one might consider that the author is trying to spice up mathematics by applying…
This paper summarizes the author's insights and experiences of teaching mathematics to incarcerated students within the U.S. prison system.
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
Recent lab experiments by Traulsen et al. for the spatial prisoner's dilemma suggest that exploratory behavior of human subjects prevents cooperation through neighborhood interactions over experimentally accessible time spans. This…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
The aim of this paper is to introduce a logic in which nouns and verbs are handled together as a deductive reasoning, and also to observe the relationship between nouns and verbs as well as between logics and conversations.
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
Riddle-solving requires advanced reasoning skills, pushing LLMs to engage in abstract thinking and creative problem-solving, often revealing limitations in their cognitive abilities. In this paper, we examine the riddle-solving capabilities…
Large Reasoning Models (LRMs) have exhibited extraordinary prowess in tasks like mathematics and coding, leveraging their advanced reasoning capabilities. Nevertheless, as these capabilities progress, significant concerns regarding their…
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…
CAPTCHAs have long been essential tools for protecting applications from automated bots. Initially designed as simple questions to distinguish humans from bots, they have become increasingly complex to keep pace with the proliferation of…
Humans can generate reasonable answers to novel queries (Schulz, 2012): if I asked you what kind of food you want to eat for lunch, you would respond with a food, not a time. The thought that one would respond "After 4pm" to "What would you…
This work delves into the realm of logic puzzles by focusing on the Knight and Knave problems popularized by Raymond Smullyan in his book series "What is the Name of This Book?". The puzzles revolve around characters known as Knights…
We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra…
I introduce, solve and generalize a new coin puzzle that involves parallel weighings.
The purpose of this article is to incite clever ways to attack problems. It advocates in favor of more elegant algorithms, in place of brute force (albeit its very well crafted) usages.