Related papers: Solving The Hardest Logic Puzzle Ever and its gene…
In 2022, Olivier Longuet, a French mathematics teacher, created a game called the \textit{calissons puzzle}. Given a triangular grid in a hexagon and some given edges of the grid, the problem is to find a calisson tiling such that no input…
Twenty questions is a widely popular verbal game. In recent years, many computerized versions of this game have been developed in which a user thinks of an entity and a computer attempts to guess this entity by asking a series of…
In 1982, Raymond Smullyan published an article, "The Asylum of Doctor Tarr and Professor Fether," that consists of a series of puzzles. These were later reprinted in the anthology, "The Lady or The Tiger? and Other Logic Puzzles." The last…
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed.…
The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer…
The game of Othello is one of the world's most complex and popular games that has yet to be computationally solved. Othello has roughly ten octodecillion (10 to the 58th power) possible game records and ten octillion (10 to the 28th power)…
Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the Algebra of Logic of the 19th century. Schr\"oder investigated it as Aufl\"osungsproblem (solution problem). It is closely related to the modern…
Existing reasoning benchmarks for large language models (LLMs) frequently fail to capture authentic creativity, often rewarding memorization of previously observed patterns. We address this shortcoming with Sudoku-Bench, a curated benchmark…
Vision-Language Models (VLMs) excel at many multimodal tasks, yet their cognitive processes remain opaque on complex lateral thinking challenges like rebus puzzles. While recent work has demonstrated these models struggle significantly with…
Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the…
Large language models (LLMs) such as GPT, Gemini, and Claude often appear adept at solving classic logic puzzles--but how much genuine reasoning underlies their answers? Recent evidence suggests that these models frequently rely on…
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…
Exploring the capabilities of Large Language Models (LLMs) in puzzle solving unveils critical insights into their potential and challenges in AI, marking a significant step towards understanding their applicability in complex reasoning…
We will extend the well-known Church encoding of Boolean logic into $\lambda$-calculus to an encoding of McCarthy's $3$-valued logic into a suitable infinitary extension of $\lambda$-calculus that identifies all unsolvables by $\bot$, where…
A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity…
The problem of the malicious ma\^{i}tre d' is introduced and solved by Peter Winkler in his book Mathematical Puzzles: A Connoisseur's Collection [1]. This problem is about a ma\^{i}tre d' seating diners around a table, trying to maximize…
Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and…
Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Existing benchmarks for frontier models often test specialized, "PhD-level" knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark with 613 problems based on the NPR Sunday Puzzle Challenge that requires…