Related papers: Minuet: A method to solve Sudoku puzzles by hand
In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…
This paper covers a variety of mathematical folk puzzles, including geometric (Tangrams, dissection puzzles), logic, algebraic, probability (Monty Hall Problem, Birthday Paradox), and combinatorial challenges (Eight Queens Puzzle, Tower of…
Encryption and Decryption is the process of sending a message in a ciphered way that appears meaningless and could be deciphered using a key for security purposes to avoid data breaches. This paper expands on the previous work on…
Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…
The joint bidiagonalization process of a matrix pair $\{A,L\}$ can be used to develop iterative regularization algorithms for large scale ill-posed problems in general-form Tikhonov regularization…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians. The program is…
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game…
K-means clustering is an unsupervised clustering method that requires an initial decision of number of clusters. One method to determine the number of clusters is the elbow method, a heuristic method that relies on visual representation.…
While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…
A new method is introduced for solving Laplace problems on 2D regions with corners by approximation of boundary data by the real part of a rational function with fixed poles exponentially clustered near each corner. Greatly extending a…
We propose a method to exponentially speed up computation of various fingerprints, such as the ones used to compute similarity and rarity in massive data sets. Rather then maintaining the full stream of $b$ items of a universe $[u]$, such…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
In this paper, we examine linguistic puzzles used in high school linguistics competitions, focusing on two common formats: Rosetta Stone and Match-Up. We propose a systematic procedure for converting existing Rosetta Stone puzzles into…
Neural models and symbolic algorithms have recently been combined for tasks requiring both perception and reasoning. Neural models ground perceptual input into a conceptual vocabulary, on which a classical reasoning algorithm is applied to…
We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures is computation of a quotient for long division. We give…
The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the…