Related papers: Solving The Hardest Logic Puzzle Ever and its gene…
A sliding puzzle is a combination puzzle where a player slide pieces along certain routes on a board to reach a certain end-configuration. In this paper, we propose a novel measurement of complexity of massive sliding puzzles with…
Frontier language models demonstrate increasing ability at solving reasoning problems, but their performance is often inflated by circumventing reasoning and instead relying on their expanding knowledge and memorisation capacity. We…
People often ask questions with false assumptions, a type of question that does not have regular answers. Answering such questions requires first identifying the false assumptions. Large Language Models (LLMs) often generate misleading…
Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein…
The 3n+1, or Collatz problem, is one of the hardest math problems, yet still unsolved. The Collatz conjecture is to prove or disprove that the Collatz sequences COL(n) always eventually reach the number of 1, for all n belongs to N+ (all…
Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1 conjecture. I agree, but very soon it will be! With the exponential growth of computer-generated mathematics, we (or rather our silicon brethrern) would have a shot at…
We consider a puzzle such that a set of colored cubes is given as an instance. Each cube has unit length on each edge and its surface is colored so that what we call the Surface Color Condition is satisfied. Given a palette of six colors,…
Fifteen Puzzle problem is one of the most classical problems that have captivated mathematical enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 1013 states that have to be explored and…
Large language models (LLMs) have demonstrated potential in reasoning tasks, but their performance on linguistics puzzles remains consistently poor. These puzzles, often derived from Linguistics Olympiad (LO) contests, provide a minimal…
Cryptic crosswords are puzzles that rely on general knowledge and the solver's ability to manipulate language on different levels, dealing with various types of wordplay. Previous research suggests that solving such puzzles is challenging…
While extremely powerful and versatile at various tasks, the thinking capabilities of large language models (LLMs) are often put under scrutiny as they sometimes fail to solve problems that humans can systematically solve. However, recent…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a…
The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they…
We believe, in the sense of supporting ideas and considering them correct while dismissing doubts about them. We take sides about ideas and theories as if that was the right thing to do. And yet, from a rational point of view, this type of…
The Connections puzzle is a word association game published daily by The New York Times (NYT). In this game, players are asked to find groups of four words that are connected by a common theme. While solving a given Connections puzzle…
As language models master existing reasoning benchmarks, we need new challenges to evaluate their cognitive frontiers. Puzzle-solving events are rich repositories of challenging multimodal problems that test a wide range of advanced…
A riddle is a question or statement with double or veiled meanings, followed by an unexpected answer. Solving riddle is a challenging task for both machine and human, testing the capability of understanding figurative, creative natural…
Higher-dimensional sliding puzzles are constructed on the vertices of a $d$-dimensional hypercube, where $2^d-l$ vertices are distinctly coloured. Rings with the same colours are initially set randomly on the vertices of the hypercube. The…