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Journal articles on the topic 'Sudoku'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

DRÁPAL, ALEŠ, and PETR VOJTĚCHOVSKÝ. "DIVISION SUDOKUS: INVARIANTS, ENUMERATION, AND MULTIPLE PARTITIONS." Glasgow Mathematical Journal 62, no. 3 (2019): 600–630. http://dx.doi.org/10.1017/s0017089519000375.

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AbstractA division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich in sudoku partitions.

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2

Nishikawa, Kohei, and Takahisa Toda. "Exact Method for Generating Strategy-Solvable Sudoku Clues." Algorithms 13, no. 7 (2020): 171. http://dx.doi.org/10.3390/a13070171.

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A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introduce a rigorous framework to discuss solvability for Sudoku instances with respect to strategies. This allows us to handle not only known strategies but also general strategies under a few reasonable assumptions. We propose an exact method for determining Sudoku clues for a given set of clue positions that is solvable with a given set of strategies.

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3

Guns, Tias, Emilio Gamba, Maxime Mulamba, Ignace Bleukx, Senne Berden, and Milan Pesa. "Sudoku Assistant – an AI-Powered App to Help Solve Pen-and-Paper Sudokus." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 13 (2023): 16440–42. http://dx.doi.org/10.1609/aaai.v37i13.27072.

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The Sudoku Assistant app is an AI assistant that uses a combination of machine learning and constraint programming techniques, to interpret and explain a pen-and-paper Sudoku scanned with a smartphone. Although the demo is about Sudoku, the underlying techniques are equally applicable to other constraint solving problems like timetabling, scheduling, and vehicle routing.

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4

Palomo, Miguel G. "Sudoku Ripeto." ICGA Journal 43, no. 1 (2021): 26–49. http://dx.doi.org/10.3233/icg-210180.

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We present a variant of Sudoku called Sudoku Ripeto. It seems to be the first to admit any combination of repeated symbols, and includes Sudoku as a proper subset. We present other Sudoku Ripeto families, each with a different repetition pattern. We define Sudoku Ripeto squares and puzzles, prove several solving rules that generalize those for Sudoku, and give sufficient conditions to flexibly solve puzzles with rules only, without search.

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Guven, Yildiz, Cihat Gültekin, and A. Beyzanur Dedeoğlu. "Comparison of Sudoku Solving Skills of Preschool Children Enrolled in the Montessori Approach and the National Education Programs Yıldız Güven1, Cihat Gültekin1, A. Beyzanur Dedeoğlu1." Journal of Education and Training Studies 8, no. 3 (2020): 32. http://dx.doi.org/10.11114/jets.v8i3.4620.

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According to Johnson-Laird (2010), sudoku, a mind game, is based on a pure deduction and reasoning processes. This study analyzed sudoku solving skills of preschool children and to ascertain whether there was a difference between children who were educated according to the Ministry of Education preschool education program and the Montessori approach. Sudoku skills of children were analyzed by gender, age, duration of preschool attendance, mother’s and father’s education level and previous experience of playing sudoku using a 12-question Sudoku Skills Measurement Tool developed for this researc

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6

Schreiner, Axel T., and James E. Heliotis. "Sudoku." ACM SIGCSE Bulletin 40, no. 2 (2008): 44–47. http://dx.doi.org/10.1145/1383602.1383632.

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7

Jones, Siân K., Stephanie Perkins, and Paul A. Roach. "The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group." International Journal of Combinatorics 2012 (November 7, 2012): 1–6. http://dx.doi.org/10.1155/2012/760310.

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A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given.

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8

Burgess, David L. "Lessons from Sudoku." EDFA Technical Articles 8, no. 1 (2006): 25–28. http://dx.doi.org/10.31399/asm.edfa.2006-1.p025.

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Abstract Failure analysis requires a working knowledge of physics, technology, materials, manufacturing practices, analytical techniques, and more. It is difficult to imagine what failure analysis would be like if all the laws of physics were perfectly apparent and all the challenges of sample preparation and testing were removed. Eliminating those considerations, failure analysis would be more like Sudoku. Sudoku is a simple number puzzle enjoyed by both children and adults. The simplicity of Sudoku compared to failure analysis is the point. Although Sudoku is starkly simple, the process is c

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9

Mat Diah, Norizan, Syahirul Riza, Suzana Ahmad, Norzilah Musa, and Shakirah Hashim. "Sudoku solutions: a comparative analysis of breadth-first search, depth-first search, and human approaches." Journal of Education and Learning (EduLearn) 19, no. 1 (2025): 561–69. http://dx.doi.org/10.11591/edulearn.v19i1.21214.

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Sudoku is a puzzle that has a unique solution. No matter how many methods are used, the result will always be the same. The player thought that the number of givens or clues, the initial value on the Sudoku puzzles, would significantly determine the difficulty level, which is not necessarily correct. This research uses two search algorithms, breadth-first search (BFS) and depth-first search (DFS), to solve a set of Sudoku puzzles based on the number of givens. The Sudoku puzzles are chosen based on the number of givens between 32 and 35. In cases where Sudoku puzzles are considered medium or i

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10

Dinata, Eric, Herman Budianto, and Hendrawan Armanto. "Hyper Sudoku Solver dengan Menggunakan Harris Hawks Optimization Algorithm." Journal of Intelligent System and Computation 2, no. 1 (2021): 20–27. http://dx.doi.org/10.52985/insyst.v2i1.153.

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Sudoku merupakan salah satu permainan klasik yang digemari banyak orang. Sebagai salah satu permainan papan, Sudoku mempunyai banyak varian, salah satunya Hyper Sudoku. Hyper Sudoku mempunyai tingkat kesulitas yang lebih tinggi daripada Sudoku biasa. Tingkat kompleksitas yang tinggi membuat pemainan ini menjadi brain teaser yang baik dan sangat cocok diambil sebagai media untuk menguji algoritma metaheuristik. Algoritma yang populer pada dekade terakhir ini adalah algoritma metaheuristik berbasis populasi, yang mengadaptasi perilaku binatang dalam memecahkan permasalahan optimasi, salah satuny

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Indriyono, Bonifacius, Natalinda Pamungkas, Zudha Pratama, Ery Mintorini, Imelda Dimentieva, and Pita Mellati. "Comparative Analysis of the Performance Testing Results of the Backtracking and Genetics Algorithm in Solving Sudoku Games." International Journal of Artificial Intelligence & Robotics (IJAIR) 5, no. 1 (2023): 29–35. http://dx.doi.org/10.25139/ijair.v5i1.6501.

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Games that hone thinking skills and logical accuracy have recently been very popular. One of them is the game Sudoku. Sudoku is a game that hones logic through puzzles arranged in rows and columns. Sudoku is also defined as a puzzle game that aims to arrange several numbers in a grid from one to nine on a grid consisting of 9x9 squares. The concept of this Sudoku game is to enter numbers into the rows and columns provided. The rule of this game is that the numbers arranged on the board cannot be the same in every row, column, and 3x3 square in the grid. In another sense, each number entered mu

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12

Hoffman, Dean. "Super Sudoku Squares." Communications on Number Theory and Combinatorial Theory 1, no. 1 (2020): 1–8. http://dx.doi.org/10.70013/wpbj2rt4.

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We refer to a completed Sudoku puzzle as a Sudoku Square of order 3. We define a more restricted, but natural, extension --- a Super Sudoku Square of order n, and determine for which orders n one exists.

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13

Soto, Ricardo, Broderick Crawford, Cristian Galleguillos, Fernando Paredes, and Enrique Norero. "A Hybridalldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles." Computational Intelligence and Neuroscience 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/286354.

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The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling an2 × n2grid, composed ofncolumns,nrows, andnsubgrids, each one containing distinct integers from 1 ton2. Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with thealldifferentglobal constraint from the constraint programming world. Thealldifferentconstraint is known to be efficient for domai

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14

Umar Khan, Muhammad, Muaaz Mulla, and Dr M. Upendra Kumar. "Optimized real-time sudoku puzzle solving and solution overlay on images and videos using advanced computer vision and TensorFlow." International Journal of Multidisciplinary Research and Growth Evaluation 5, no. 1 (2024): 66–70. http://dx.doi.org/10.54660/.ijmrge.2024.5.1.66-70.

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This paper presents a novel approach to solving Sudoku puzzles using computer vision techniques. Sudoku, a popular logic-based number placement game, poses an interesting challenge for automated solutions. The proposed Sudoku solver employs image processing and computer vision algorithms to extract the puzzle grid from a given image. The system then employs optical character recognition (OCR) to recognize and digitize the numbers within the grid. The image preprocessing involves techniques such as edge detection, contour identification, and perspective transformation to enhance the accuracy of

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15

Buckley, Carol A. "Using Sudoku Bulletin Boards to Teach Mathematical Reasoning." Teaching Children Mathematics 15, no. 4 (2008): 208–11. http://dx.doi.org/10.5951/tcm.15.4.0208.

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“Maddening!” “Addicting!” “Can't do it.” “Do it every day.” These are phrases my peers have used in reference to Sudoku puzzles. I enjoy completing Sudoku puzzles but had not previously considered that incorporating them into my instruction would motivate my primary-grades students. After reading “Exploring the Sudoku Challenge” (Wilburne 2006), I decided to offer Sudoku as a student option for the logical reasoning category of a tic-tac-toe instructional strategy. In a tic-tac-toe strategy, three tasks in three different categories are organized to resemble a tic-tac-toe board. Students choos

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16

Hanafi, Alya Aulia, Naseh Hibban, Fawwaz Muhammad Zulfikar, and Faisal Dharma Adhinata. "Penyelesaian Permainan Sudoku Menggunakan Algoritma Backtracking Berbasis Artificial Intelligence." Journal ICTEE 2, no. 2 (2021): 50. http://dx.doi.org/10.33365/jictee.v2i2.1288.

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Kebutuhan teknologi untuk mempermudah dan menyelesaikan suatu permasalahan menjadi efisien sangat diperlukan di era modern ini. Salah satu bidang ilmu yang sering digunakan untuk memecahkan masalah dengan meniru kebiasaan manusia adalah Artificial Intelligence (AI). Permainan Sudoku merupakan permainan dengan jenis teka teki logika. Sudoku termasuk pada permasalahan NP – complete, sehingga sulit atau bahkan tidak bisa untuk diselesaikan dengan waktu yang sama. Dari permasalahan tersebut, dibutuhkan sebuah algoritma AI untuk menyelesaikan Permainan Sudoku. Salah satu algoritmanya adalah Backtra

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17

Lee, Sang-Un. "Sudoku Algorithm." Journal of the Institute of Webcasting, Internet and Telecommunication 15, no. 1 (2015): 207–15. http://dx.doi.org/10.7236/jiibc.2015.15.1.207.

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18

Aaronson, L. "Sudoku Science." IEEE Spectrum 43, no. 2 (2006): 16–17. http://dx.doi.org/10.1109/mspec.2006.1584356.

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19

Lindgren, William. "Mathematical Sudoku." Math Horizons 15, no. 2 (2007): 21. http://dx.doi.org/10.1080/10724117.2007.11974739.

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20

Philip Riley and Laura Taalman. "Tetris Sudoku." College Mathematics Journal 44, no. 4 (2013): 292. http://dx.doi.org/10.4169/college.math.j.44.4.292.

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21

Indriyono, Bonifacius Vicky, Ratna Wardani, Titin Susanti, et al. "Analysis of the Concept of Solving the Sudoku Game Using Backtracking and Brute Force Algorithms." International Journal of Artificial Intelligence & Robotics (IJAIR) 6, no. 1 (2024): 40–47. http://dx.doi.org/10.25139/ijair.v6i1.8377.

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Sudoku is a puzzle game that arranges numbers from one to nine on a board consisting of 9x9 squares. This game has a rule: the numbers arranged on a board cannot be the same in each row or column. The main goal of this Sudoku game is to complete the board and win by entering numbers into each empty box. Therefore, in this Sudoku game, there is only one valid solution. At the start of the game, several numbers are provided, which serve as clues for players to fill in the next box. The number of clues at the start of the game determines whether the Sudoku game level is difficult. The fewer the c

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22

Pu-Sheng Tsai, Pu-Sheng Tsai, Ter-Feng Wu Pu-Sheng Tsai, Jen-Yang Chen Ter-Feng Wu, and Jen-Feng Huang Jen-Yang Chen. "Integrating of Image Processing and Number Recognition in Sudoku Puzzle Cards Digitation." 網際網路技術學刊 23, no. 7 (2022): 1573–84. http://dx.doi.org/10.53106/160792642022122307012.

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<p>The aim of Sudoku puzzle is to fill in the blank cells in a square matrix consisting of nine 3x3 blocks with the numbers 1-9 in a way that no number appears more than once in any row, column, or block. We combined image processing, a convolutional neural network (CNN), and a Sudoku game algorithm to automatically place the numbers 1-9 in the blank cells of a Sudoku square matrix. An image of the Sudoku square matrix is first captured using a camera, and then the vertical lines, horizontal lines, and outer frame of the Sudoku square matrix are detected using Hough transform (HT). Based

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23

Adhawina, Raissya, Stevania Sri Debbye Simbolon, Sri Lestari Manurung, Jesiska Anjelin Siagian, and Cut Rania Andini. "Strategi Matematis Penyelesaian Sudoku Berbasis Grup Permutasi." Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika 8, no. 2 (2025): 580–87. https://doi.org/10.30605/proximal.v8i2.5684.

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Sudoku adalah permainan logika berbasis angka yang dapat direpresentasikan sebagai masalah kombinatorika kompleks dengan strategi penyelesaian berbasis teori grup permutasi. Penelitian ini bertujuan menganalisis strategi penyelesaian Sudoku menggunakan teori grup permutasi dan membandingkannya dengan metode backtracking. Metode penelitian yang digunakan adalah kualitatif deskriptif dengan studi literatur sebagai teknik pengumpulan data. Analisis dilakukan terhadap konsep grup permutasi dalam Sudoku, struktur angka dalam permainan, serta penerapan operasi permutasi dalam strategi penyelesaian.

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24

Laela, Kumala Vadilatu, Mohamad Fatih, and Khoirul Wafa. "Pengembangan LKPD Berbasis Permainan Sudoku Kata Materi Ciri-Ciri Makhluk Hidup Untuk Meningkatkan Kemandirian Belajar Siswa Kelas III UPT SD Negeri Sawentar 04 Kanigoro Blitar." Al-Madrasah: Jurnal Pendidikan Madrasah Ibtidaiyah 8, no. 4 (2024): 1619. http://dx.doi.org/10.35931/am.v8i4.4098.

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<p>LKPD yaitu lembaran dokumen yang berisi kegiatan yang dilaksanakan oleh siswa. Kegiatan pada LKPD ini adalah Permainan Sudoku Kata. Permainan Sudoku Kata adalah permainan menyusun kata supaya dalam 1 baris dan 1 kolom tidak ada kata yang berulang. Permainan Sudoku Kata diharapkan dapat meningkatkan kemandirian belajar siswa. LKPD berbasis Permainan Sudoku Kata merupakan produk yang diciptakan dari hasil penelitian ini yang digunakan sebagai bahan ajar di kelas III yang digunakan untuk memperoleh peningkatan kemandirian belajar siswa. Hal ini juga merupakan tujuan dari penelitian ini,

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Manisha. "Sudoku Solver – A Novel Approach Using Recognition of Printed Text Image." Journal of Computer Science and Technology Studies 6, no. 4 (2024): 38–46. http://dx.doi.org/10.32996/jcsts.2024.6.4.6.

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Detecting and analyzing text in multimedia is required for recognition of characters which can be used for performing multi-objectives in numerous research areas and applications. Characters or numbers in images can be hand-written, printed document, typewritten or artificially added for the purpose of searching or indexing, editing or image understanding. Various applications such as License Plate Detection, Handwritten documents recognition, Sudoku Solving, multi-oriented recognition focuses on character recognition. Image Sudoku solver works on Sudoku puzzle images. In this paper, the print

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Li, Hongyi, Qisheng Li, and Zujun Ou. "Construction of Sudoku designs and Sudoku-based uniform designs." Statistics & Probability Letters 89 (June 2014): 51–57. http://dx.doi.org/10.1016/j.spl.2014.02.016.

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Mishra, Priyanka, and Rakesh Ahuja. "A Novel Image Watermarking Method Against Crop Attack Using Two-Step Sudoku Puzzle." ECS Transactions 107, no. 1 (2022): 8351–60. http://dx.doi.org/10.1149/10701.8351ecst.

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Digital image watermarking is used to secure the digital images. There are several methods for securing the images. But there is probability to destroy the information by an attacker. Attacker can damage even a single segment of watermark image. There are many techniques to overcome from several attacks through which the cropped section of an image can be recover and there is no need to detect watermark. A robust image watermarking method against various cropping attack by the use of Sudoku puzzle is suggested in this paper. This method is build upon the attributes of permutation of Sudoku mat

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Paramadevan, Paramacutty. "A Binary Integer Programming Approach to find a Sudoku Matrix." Vavuniya Journal of Science 1, no. 1 (2022): 26–30. http://dx.doi.org/10.4038/vjs.v1i1.4.

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In the basic Sudoku game, players must fill the entries of a n × n matrix, except some given entries, under the conditions that each row, each column, and each m × m sub matrix contains integers 1 through n exactly once. In this research paper, in addition to the basic game, conditions and solution process for three advanced versions, such as Sudoku X, Four Square Sudoku and Four Pyramid Sudoku were also studied. In this study, the above-mentioned conditions are converted into appropriate mathematical forms as constraints of the Integer Linear Programming Problem using Pascal Programming Langu

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Singh, Varun, Varun Sharma, and Vasu Bachchas. "Sudoku Solving Using Quantum Computer." International Journal for Research in Applied Science and Engineering Technology 11, no. 2 (2023): 622–29. http://dx.doi.org/10.22214/ijraset.2023.49094.

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Abstract: We use ability of quantum computing such as superposition and entanglement to solve the sudoku. In recent years, quantum computers have shown promise as a new technology for solving complex problems in various fields, including optimization and cryptography. In this paper, we investigate the potential of quantum computers for solving Sudoku puzzles. We present a quantum algorithm for solving Sudoku puzzles, and compare its performance to classical algorithms. Our results show that the quantum algorithm outperforms classical algorithms in terms of both speed and accuracy, and provides

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Lina, Tirsa Ninia, and Matheus Supriyanto Rumetna. "Comparison Analysis of Breadth First Search and Depth Limited Search Algorithms in Sudoku Game." Bulletin of Computer Science and Electrical Engineering 2, no. 2 (2021): 74–83. http://dx.doi.org/10.25008/bcsee.v2i2.1146.

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Sudoku is a game that sharpens the brain and is very well known. But the problem faced in this condition is how we can find a solution for the completion of this game. Problems with the Sudoku game can be solved by using the concept of Artificial Intelligence (AI). Some of the algorithms that can be used are the Breadth First Search (BFS) and Depth Limited Search (DLS) algorithms. The purpose of this research is to find a solution for Sudoku and make a comparative analysis of the search results of the two algorithms. The results obtained are application design in the form of a simulation of th

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Dauran, N. S., A. B. Odeyale, and A. Shehu. "CONSTRUCTION AND ANALYSIS OF BALANCED INCOMPLETE SUDOKU SQUARE DESIGN." FUDMA JOURNAL OF SCIENCES 4, no. 2 (2020): 290–99. http://dx.doi.org/10.33003/fjs-2020-0402-219.

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Sudoku squares have been widely used to design an experiment where each treatment occurs exactly once in each row, column or sub-block. For some experiments, the size of row (or column or sub-block) may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Sudoku squares design (BISSD) is proposed. A general method for constructing BISSD is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Sudoku designs. The relative efficiencies of a delete-one-tr

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Jonas Reycian B. Saraosos and Michael Anthony Jay B. Regis. "Development of an Android-Based Visual Sudoku Solver Using Contour Finding and Backtracking Algorithm." Journal of Science, Engineering and Technology (JSET) 6, no. 1 (2018): 208–17. http://dx.doi.org/10.61569/pw8s6r19.

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This study developed an Android application that automatically solves Sudoku puzzle. An image of the Sudoku puzzle is either captured by the built-in camera or loaded directly from the media gallery. Contour finding algorithm and Hough transform would detect the game board. The givens (i.e. number that exist in a Sudoku board) are acquired by dividing the entire game board by 81 cells with the contour finding algorithm extracting the particular given. Identification is done using the Tesseract – Optical Character Recognition (OCR). Backtracking algorithm calculated the solution and displayed i

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Sahib, Ghazala, Sajjad Ahmad, and Sundus Hussain. "Construction And Analysis Of Hyper Block Graeco Latin Sudoku Square Design." Metallurgical and Materials Engineering 31, no. 4 (2025): 1093–109. https://doi.org/10.63278/mme.v31i4.1729.

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A novel experimental design called Hyper Block Graeco Latin Sudoku Square Design (Hyper Block GLaSS Design) has been released. It applies the row blocking and column blocking features of Subramani and Pormuswamy Sudoku Square Designs. The Error Sum of Square is decreased by implementing the Block Sum of Square for both rows and columns. Hyper Block GLaSS Design aims to investigate eight parameters and test three sets of treatments concurrently in a single experiment. For Hyper Block GLaSS Design a numerical example is used to analyze the fixed effect model's construction, compare it to the Hyp

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Finlayson, Graham, and Seth Nixon. "Sudoku Texture Classification." Electronic Imaging 2016, no. 14 (2016): 1–5. http://dx.doi.org/10.2352/issn.2470-1173.2016.14.ipmva-389.

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Makzhanova, Yana V. "SUDOKU WITH INTEGRALS." Bulletin of the Moscow State Regional University (Pedagogics), no. 4 (2017): 38–44. http://dx.doi.org/10.18384/2310-7219-2017-4-38-44.

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Eichelkraut, Toni, and Alexander Szameit. "Random sudoku light." Nature 526, no. 7575 (2015): 643–44. http://dx.doi.org/10.1038/526643a.

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37

Allen, Margaret. "Sudoku and fairytales." 5 to 7 Educator 2005, no. 11 (2005): 18–19. http://dx.doi.org/10.12968/ftse.2005.4.11.19658.

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Wilson, Peter. "The sudoku bundle." Zpravodaj Československého sdružení uživatelů TeXu 20, no. 3 (2010): 227–41. http://dx.doi.org/10.5300/2010-3/227.

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Taalman, Laura. "Taking Sudoku Seriously." Math Horizons 15, no. 1 (2007): 5–9. http://dx.doi.org/10.1080/10724117.2007.11974720.

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Moon, Todd K., Jacob H. Gunther, and Joseph J. Kupin. "Sinkhorn Solves Sudoku." IEEE Transactions on Information Theory 55, no. 4 (2009): 1741–46. http://dx.doi.org/10.1109/tit.2009.2013004.

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Shrout, J. D. "Solving Pathogen Sudoku." Science Translational Medicine 5, no. 166 (2013): 166ec2. http://dx.doi.org/10.1126/scitranslmed.3005530.

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Voth, H. J. "Clark's intellectual Sudoku." European Review of Economic History 12, no. 2 (2008): 149–55. http://dx.doi.org/10.1017/s1361491608002190.

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Saecker, Mary. "Chemistry Sudoku Puzzle." Journal of Chemical Education 84, no. 4 (2007): 577. http://dx.doi.org/10.1021/ed084p577.

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MacHale, Des, and Peter MacHale. "96.23 Minimal Sudoku." Mathematical Gazette 96, no. 535 (2012): 153–56. http://dx.doi.org/10.1017/s002555720000423x.

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Wu, Jiann-Ming, Pei-Hsun Hsu, and Cheng-Yuan Liou. "Sudoku associative memory." Neural Networks 57 (September 2014): 112–27. http://dx.doi.org/10.1016/j.neunet.2014.05.023.

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DEMOEN, BART, and MARIA GARCIA DE LA BANDA. "Redundant Sudoku rules." Theory and Practice of Logic Programming 14, no. 3 (2012): 363–77. http://dx.doi.org/10.1017/s1471068412000361.

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AbstractThe rules of Sudoku are often specified using 27 all_different constraints, referred to as the big constraints. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: Many subsets of six of these big constraints are redundant (i.e., they are entailed by the remaining 21 constraints), and six is maximal (i.e., removing more than six constraints is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the small constraints, is stated as a conjecture.

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Elsholtz, Christian, and Annette Mütze. "Sudoku im Mathematikunterricht." Mathematische Semesterberichte 54, no. 1 (2007): 69–93. http://dx.doi.org/10.1007/s00591-006-0014-7.

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48

Burgess, David L. "Lessons from Sudoku." Journal of Failure Analysis and Prevention 6, no. 3 (2006): 35–38. http://dx.doi.org/10.1007/bf02692326.

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Lorch, John, and Ellen Weld. "Modular magic sudoku." Involve, a Journal of Mathematics 5, no. 2 (2012): 173–86. http://dx.doi.org/10.2140/involve.2012.5.173.

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Najafian, Mehrab, T. Aaron Gulliver, and Morteza Esmaeili. "Construction of Standard Solid Sudoku Cubes and 3D Sudoku Puzzles." IEEE Access 10 (2022): 30180–88. http://dx.doi.org/10.1109/access.2022.3159027.

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