Relevant bibliographies by topics / Sudoku puzzle

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Sudoku puzzle'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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Journal articles on the topic "Sudoku puzzle"

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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 intermediate difficulty, the solutions generated by both algorithms will be compared with the human-solving approach. The research aims to determine whether humans tend to solve Sudoku puzzles with solutions resembling those generated by BFS or DFS. Furthermore, if all three approaches-human, BFS, DFS-yield comparable solutions, the Sudoku puzzle has only one unique solution.
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Chen, Kaiqi. "Exploring A Better Way to Constraint Propagation Using Naked Pair." ITM Web of Conferences 70 (2025): 04025. https://doi.org/10.1051/itmconf/20257004025.

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Sudoku is an NP-complete problem therefore developing various efficient algorithms is crucial. This paper presents an enhanced approach to solving sudoku puzzles by improving on recursive backtracking with constraint propagation and bitmask, focusing on the implementation of the naked pair technique. This research aims to add constraints to reduce the backtracking steps in solving sudoku using naked pairs, which is a technique that eliminates candidates of a cell from other cells in the same row, column or sub-grid when two cells share the same candidate sets. This research uses a dataset of 1 million sudoku puzzlers from Kaggle to evaluate the proposed solver’s performance. The solver first processes the puzzle into bitmask vectors then uses the singles and naked pairs technique to minimize the candidates, and then uses depth-first search to backtrack and solve the puzzle. As a result, the naked pair strategy slightly increases the total steps, and it significantly reduces the computation of depth-first search steps, making the solver potentially more efficient in solving difficult puzzles.
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G M, Ananya, and Ankit Kumar Singh. "Augmented Reality Sudoku Solver." ECS Transactions 107, no. 1 (2022): 2085–93. http://dx.doi.org/10.1149/10701.2085ecst.

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Solving Sudoku puzzles is now made easy through a few mobile applications. However, these applications fail to provide a fast and accurate solution. Computer Vision and Deep Learning have advanced to a level where another dimension for solving such puzzles has been added. The paper aims to propose a novel method to generate the solution of Sudoku puzzles and to display it using Augmented Reality. The Sudoku puzzle is recognized over several image processing phases, followed by recognition of letters using Deep Learning. The captured puzzle is then solved by a solver written in Rust. Eventually, the resultant mask of the solution is merged with the original image by computer vision and uses Augmented Reality to render the solution. The end-to-end pipeline takes milliseconds before an accurate final solution is obtained. The solver is extremely reliable in terms of precision and speed.
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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 grid extraction. Subsequently, OCR is applied to recognize the digits within each cell of the Sudoku grid. The solver then utilizes a backtracking algorithm to systematically fill in the missing numbers while adhering to the rules of Sudoku. The computer vision-based Sudoku solver offers advantages in terms of versatility, as it can handle puzzles of varying difficulty levels and appearances. The system's performance is evaluated on a diverse set of Sudoku puzzles, demonstrating its effectiveness in accurately solving puzzles with different grid sizes and layouts. The results indicate that the proposed approach achieves competitive solving times while maintaining a high level of accuracy. The presented Sudoku solver serves as a testament to the potential of computer vision in solving complex puzzles, opening avenues for further research in the integration of artificial intelligence and image processing for recreational problem-solving applications.
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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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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 challenging to the best of us. Good and bad problem-solving practices are clearly exposed by the experience of solving a few Sudoku puzzles. Some insights that are brilliantly clear in Sudoku are equally true in failure analysis.
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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 printed text Sudoku image is used as the input. The image is enhanced by filling the horizontal and vertical gaps in the grids that may occur due to shadow or distortion of the scanned image such that all the 81 grids are extracted. Secondly, the numbers and grids in the enhanced image are extracted and a dancing link approach using Algorithm X is adopted to solve the Sudoku. The proposed work is compared with a backtracking approach and dancing link approach without enhancing the image and its computation time for various ranks of difficulty of a puzzle taken. The Sudoku puzzle can be used to secure information stored in an image as the number of solutions to solve a Sudoku puzzle is very large, allowing it to be used as a security tool resistant to brute force attacks.
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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 on the OpenCV module, we proposed an image processing algorithm that captures the numbers in the image and calculates the location coordinates of the numbers in the image. We trained the CNN using the MNIST handwritten digit dataset to recognize the numbers in the Sudoku square matrix. Finally, we used the Python programming language to design a Sudoku puzzle backtrace algorithm that automatically deduces and fills in the blank cells in the square matrix. This study provides further understanding of the critical operating principles of CNNs and lays down a foundation for future research.</p> <p> </p>
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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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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 domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods.
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Dissertations / Theses on the topic "Sudoku puzzle"

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Godinho, Cecília Solange Gomes. "Alguma da matemática do Sudoku." Master's thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/10474.

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Mestrado em Matemática e Aplicações<br>Neste trabalho o objectivo principal é fazer um estudo de alguma da Matemática presente no conhecido puzzle Sudoku. Dado que o tema da presente dissertação foi proposto a duas alunas, e como se tratava de um assunto novo para ambas, os dois primeiros capítulos resultam de um trabalho conjunto com a minha colega Andreia Cristina Dias Morgado. Os conceitos introdutórios serão apresentados no primeiro capítulo, onde se abordarão os Quadrados Latinos e as suas principais características. No segundo capítulo exibimos as aplicações dos Quadrados Latinos à Teoria de Grupos. No terceiro capítulo abordamos alguns resultados importantes no estudo das Geometrias finitas, nomeadamente no que diz respeito aos planos afins e projectivos, mostrando-se como se pode obter um deles à custa do outro. Serão abordadas também as principais relações destes planos com os Quadrados Latinos. Por fim, no quarto capítulo faz-se uma análise da relação entre as propriedades dos Quadrados Latinos e do Sudoku, desenvolvendo-se um pouco da história do aparecimento deste puzzle, o modo como se joga e os níveis de dificuldade. Além disso, serão apresentadas algumas variantes do puzzle, finalizando-se com o problema das possíveis colorações parciais de um Sudoku.<br>In this work, the main aim is to make a study of some Mathematics presents in the Sudoku puzzle we know so well. Since the theme of this dissertation was purposed to two students, and since this was a new subject for both, the first two chapters resulted from a work, made by me and my colleague Andreia Cristina Dias Morgado. The introductory concepts will be presented in the first chapter, where we will make reference to the Latin Square and its main features. In the second chapter we show the applications of Latin Squares to the Theory of Groups. In the third chapter we will present some important results of the study of finite Geometries, particularly with what is concerned to affine plans and projective plans. We show how to get one from another. It also studies the main relations of these ones with the Latin Squares. Finally, the fourth chapter is an analysis of the relation between the properties of Latin Squares and Sudoku, developing a bit of history from the beginning of this puzzle and how to play it and its difficulty levels. In addition, we will present some variants of the puzzle, ending with the problem of possible partial colorations of a Sudoku.
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Emery, Michael Ray. "Solving Sudoku Puzzles with the Cougaar Agent Architecture." Thesis, Montana State University, 2007. http://etd.lib.montana.edu/etd/2007/emery/EmeryM0807.pdf.

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The Cougaar distributed agent architecture, originally a DARPA-funded research project, provides a platform for developing distributed agent systems. Testing its ability to solve complex problems using a large number of agents in an interesting topic of research. In this thesis, the Cougaar distributed agent architecture is studied from the standpoint of Sudoku. Through analysis and experimentation, insight is gained into both the properties and weaknesses of Cougaar. Cougaar\'s performance when solving Sudoku puzzles is then compared with other Sudoku solving techniques. The Cougaar agent approach solves Sudoku puzzles in a human-like fashion, reaching solutions using both analysis and guessing. Cougaar is shown to be capable of solving Sudoku puzzles in a distributed agent architecture. Although not as fast as traditional techniques, the Cougaar distributed agent approach is able to provide solutions to Sudoku puzzles using fewer guesses. Additionally, solving Sudoku puzzles with Cougaar exposed some reliability issues and demonstrated the overhead required for communication. These results open the way for additional study of Cougaar.
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Santos, Tiago Vallejo dos. "Sudoku em FPGA." Master's thesis, Universidade de Aveiro, 2011. http://hdl.handle.net/10773/8946.

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Mestrado em Engenharia Electrónica e Telecomunicações<br>Este trabalho, desenvolvido no âmbito dos sistemas reconfiguráveis, tem como objetivo a implementação de um solucionador de puzzles Sudoku, quer em software quer em hardware, tentando minimizar o seu tempo de solução. Deste modo, foram desenvolvidos três solucionadores: Simples, apenas capaz de resolver puzzles simples, Tentativa e Erro, que implementa um algoritmo de Breadth-First Search para solucionar puzzles mais complexos, e, por fim, o solucionador Tentativa e Erro com capacidade para processamento paralelo, também este capaz de solucionar puzzles mais complexos. Todos estes solucionadores foram implementados e testados numa FPGA da família Spartan-3E da Xilinx, usando, para isso, uma placa de prototipagem da Digilent. Os resultados obtidos foram comparados entre as várias implementações abordadas, assim como com outros solucionadores existentes.<br>This work, developed in the context of reconfigurable systems, has as an objective the implementation of a Sudoku solver, both in software and hardware, and attempting to minimize its solution time. Thus, three solvers were developed: Simple, only able to solve simple puzzles, Trial and Error, which implements a Breadth-First Search algorithm, being able to solve more complex puzzles, and, finally, the Trial and Error solver with the possibility of parallel processing, being also able to solve complex puzzles. All these solvers were implemented and tested on an FPGA of Xilinx Spartan- -3E family, using for this purpose a prototyping board from Digilent. The results were compared between the various implementations, as well as with other state-of-the-art solvers.
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Ekström, Johan, та Kristofer Pitkäjärvi. "The backtracking algorithm and different representations for solving Sudoku Puzzles". Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-146016.

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Two implementations of the backtracking algorithm for solving Sudoku puzzles as well as their dependence on the representations of the problem have been studied in order to ascertain pros and cons of different approaches. For each backtracking step, empty cells could be assigned numbers sequentially or, by using a greedy heuristic, by the probability that guessed numbers were more likely to be correct. Representations of the Sudoku puzzles varied from a n2 matrix to a n3 matrix, as well as a combination of both. This study shows that (1) a sequential approach has better best case times but poor worst case behaviour, and a n3 representation does not benefit over a n2 representation; (2) a greedy heuristic approach has superior worst case times but worse best case, and n3 representations sees great benefits over n2 representations. A combination of n2 and n3 representations grants the best overall performance with both approaches.
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Wyld, Kira A. "Sudoku Variants on the Torus." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/103.

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This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.
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Lindberg, Joakim, and Martin Steier. "Efficiency of the hybrid AC3-tabu search algorithm for solving Sudoku puzzles." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-166421.

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There are many different algorithms for solving Sudoku puzzles, with one of the newer algorithms being the hybrid AC3-tabu search algorithm. Since the algorithm has not been subject of much research, the aim of this thesis is to increase the knowledge of it. This thesis evaluates the efficiency of the hybrid AC3-tabu search algorithm by analyzing how quickly it solves puzzles compared to two other solving algorithms: one using brute-force search, and one combining human solving techniques with brute-force search. This thesis also investigates if there is a correlation between the number of puzzle clues and the solving time for the hybrid AC3-tabu search algorithm. The results show that the hybrid AC3-tabu search algorithm is less efficient than the two other algorithms, and that there seems to be a correlation between the number of clues and the solving time for the algorithm. The conclusion is that due to the algorithm’s low efficiency and some of its characteristics, it is not suitable for solving Sudoku puzzles.
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Golan, Jonathan, and Joel Kallin. "Measuring Improvements and the Effects of Multiple and Unique Solution Puzzles on Sudoku Solving Algorithms." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-166739.

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In this paper we compare various Sudoku solving algorithms in order to determine what kind of run-time improvements different optimizations can give. We will also examine what kind of effect the existence of multiple solutions in the puzzles has on our result.
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Ebner, Angela Catuta Ferreira. "Jogo sudoku em crianças com 6 - 7 anos: modos de realizar, compreender e intervir." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/47/47131/tde-04072013-161239/.

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. A Escola Fundamental I tem como objetivo promover em seus alunos o desenvolvimento da capacidade de aprender e de se relacionar através da representação, da comunicação e da resolução de problemas em favor da aprendizagem da língua, da matemática, da representação espacial, temporal e gráfica. No campo da Psicologia e da Educação pesquisas demonstram que o jogo pode ser usado para criar situações-problema e assim contribuir para processos de desenvolvimento e aprendizagem em crianças e adolescentes. Esta pesquisa trata, então, de propor uma forma de intervenção que auxilie a aprendizagem da resolução de problemas, através de um jogo que implica o uso de operações lógicas. O Sudoku foi o jogo escolhido porque os problemas que ele apresenta são da natureza e uso da lógica, no sentido de que para descobrir o número de cada casa vazia o jogador deve coordenar vários aspectos ao mesmo tempo e considerar que há apenas uma resposta para cada caso. O recorte de idade feito para a presente pesquisa, crianças com 6-7 anos, se apoia na teoria piagetiana que afirma que as construções operatórias dão início, em média, aos sete anos e seguem até a vida adulta. Assim, criou-se, através de oficinas com o jogo Sudoku, situações-problema que exercitaram o uso do pensamento lógico favorecendo os processos de desenvolvimento e de aprendizagem requeridos para o alcance das expectativas previstas para sujeitos que cursam o segundo ano da Escola Fundamental I. Foram feitas 17 oficinas, sendo duas por semana e com duração de uma hora cada, em três turmas de segundo ano de uma escola particular do município de Ribeirão Preto, alcançando um total 60 participantes. A fundamentação metodológica utilizada nas oficinas se baseia nos modelos Taos, Paris, Atenas e Eldorado desenvolvidos por Gruber e Vonèche (1995) que têm como objetivo aplicar à Educação as contribuições de Piaget ao explorar o pensamento e a compreensão da criança em relação à natureza dos objetos, ao tempo, espaço, juízo moral e etc. Os dados foram analisados a partir dos seguintes eixos: 1) como os participantes resolveram e compreenderam o jogo Sudoku; 2) qual o valor das situações-problema para o primeiro eixo; 3) como e por que aplicar os Modelos Taos, Paris, Atenas e Eldorado em oficinas sobre o jogo Sudoku; e 4) como praticar uma visão construtivista, apoiada na perspectiva de Piaget, em uma situação de jogo com sujeitos de 6-7 anos. Os resultados apontam que no início do processo de intervenção poucos sujeitos conseguiam resolver o Sudoku da forma correta. No entanto, no desenrolar das oficinas foi possível identificar uma considerável aprendizagem deste jogo por parte dos participantes e, mais do que isto, observou-se um apreciável desenvolvimento dos sujeitos quanto à compreensão do jogo. Atribui-se tal desenvolvimento e aprendizagem às atividades das oficinas em resolver os jogos e às situações-problema. Conclui-se, ainda, que os modelos de Gruber e Vonèche formaram uma excelente base de intervenção para o aprendizado do jogo e de suas implicações lógicas. Assim, confiamos que tal estudo aqui apresentado possa colaborar de alguma maneira com educadores e psicólogos interessados no uso do jogo para o desenvolvimento e a aprendizagem de seus alunos e pacientes a respeito do pensamento lógico<br>Primary school has as a target the promotion of the development of its students capacity to learn and relate through representation, communication and problem solving in favor of language learning, mathematics and spatial, temporal and graphical representation. In the fields of Psychology and Education researches show that gaming can be used to create a problem situation contributing to the process of development and learning in children and teenagers. This research proposes a form of intervention that helps the learning of problem solving, through a game that implies the use of logical operations. Sudoku was the game/puzzle chosen because the problems that it presents are of logical nature and use, in a sense that for discovering the empty squares right number the player must coordinate several aspects at the same time while taking into consideration that there is only one right answer for each case. Children from 6 to 7 years old were chosen because of the Piagetian theory that states that operatory constructions begin at that age. Therefore, through Sudokus workshops problem situations were created to exercise the use of logical thought favoring the process of development and learning that is required for the achievement of expectations regarding the individuals going through the second year of primary school. Seventeen workshops of one hour each, were made twice a week, with three groups attending the second year of a private primary school in Ribeirão Preto, totaling in 60 participants. The methodological grounding was based on the models Taos, Paris, Athens and Eldorado developed by Gruber and Vonèche (1995) these models had an which was objective to apply Piagets contribution to Education as he explored a childs thought and comprehension of the nature of objects, time, moral judgement, etc. The data was analyzed through the following axes: 1) How participants solved and comprehended the Sudoku puzzle; 2) What is the value of the problem situations for the first axis; 3) How and why to apply the models Taos, Paris, Athens and Eldorado in the Sudoku workshops; and 4) How to practice a constructivist viewpoint, based on Piagets perspective, in game situations with children from 6 to 7 years old. The results demonstrate that at the beginning of the intervention few children were able to correctly solve the Sudoku puzzle. However, through the workshops a considerable amount of learning was identified, and more than that, a development of the game comprehension. The learning and development achieved is attributed to the workshops activities of puzzle solving and problem situation. We conclude that Gruber and Vonèches models formed an excellent intervention base for the learning of the puzzle and its logical implications. Therefore, we trust that the present study may collaborate in some ways with educators and psychologists interested in the use of games for their students and patients development and learning of logical thought
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Wang, Yu-Wen, and 王郁雯. "Automatic Appraisal on Challenges and Skill–Taking Puzzle Game "Sudoku" As an Example." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/qtpb3x.

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碩士<br>國立交通大學<br>多媒體工程研究所<br>100<br>How to define the difficulty of a problem? In the past, many scholars have invented a lot of ways to do it, mainly on how to solve the problem more effectively, and then according to the complexity of the method, to provide a way of assessing the degree of difficulty. However, different problems require different problem-solving skills. Therefore, it will affect the complexity of solving problems a lot. Moreover, not every computer problem-solving approach is suitable for human, in other words, it is not necessary for the average person using these skills to solve the problem. Therefore, this study attempts to think about a person in the problem solving process so as to define the difficulty of the problem from human perspective. Klein pointed out that ordinary people use common heuristic method to solve problems, such as means-end analysis and trial-and-error. For such concept, we design a Sudoku AI program to quantify the complexity of AI program. Then, we compare the actual rate of human solving time to find the formula that represents the difficulty of Sudoku. In the process of solving Sudoku, we find that branch of uncertain nodes in search tree and the times of guessing and backtracking have an impact on the difficulty of Sudoku.
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Ζώττου, Δήμητρα Νεφέλη. "Sudoku puzzles και συνδυαστικά προβλήματα". Thesis, 2012. http://hdl.handle.net/10889/6500.

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Στην παρούσα εργασία προσεγγίζονται τα Sudoku puzzles χρησιμοποιώντας μαθηματικές έννοιες κυρίως από την θεωρία γραφημάτων, την άλγεβρα, τη θεωρία πινάκων αλλά και την κρυπτογραφία και τη θεωρία ανάπτυξης αλγορίθμων, oυσιαστικά χρησιμοποιούνται διάφορες οπτικές γωνίες προκειμένου να απεικονιστεί η μελέτη αυτών των puzzles μέσω των μαθηματικών. Η εργασία χωρίζεται σε έξι βασικά κεφάλαια: Το πρώτο κεφάλαιο περιέχει βασικές έννοιες της άλγεβρας και της θεωρίας γραφημάτων, όπως ο ορισμός της ομάδας, του συνεκτικού γραφήματος, ο βαθμός κορυφής και άλλα, οι οποίες χρησιμοποιούνται επανειλημμένα στην εργασία, έτσι ώστε να μπορεί να γίνει κατανοητή χωρίς να απαιτείται η χρήση άλλων επιστημονικών πηγών. Χωρίζεται σε τέσσερεις βασικές ενότητες οι οποίες παρουσιάζονται με την ακόλουθη σειρά. Η πρώτη ενότητα είναι οι Βασικές Έννοιες Γραφημάτων, η οποία ουσιαστικά αναφέρεται στην βασική ορολογία των γραφημάτων. Η δεύτερη ενότητα είναι τα Βασικά Είδη Γραφημάτων και περιέχει γραφήματα με συγκεκριμένα χαρακτηριστικά και ιδιότητες, οι οποίες είναι απαραίτητες για την ανάλυση της παρούσας εργασίας. Στη συνέχεια η τρίτη ενότητα είναι οι Βασικές Έννοιες Γραμμικής Άλγεβρας, η οποία περιέχει συγκεκριμένους ορισμούς κυρίως των ομάδων και των συμμετριών που χρησιμοποιούνται για την απαρίθμηση των Sudoku. Τέλος η τελευταία ενότητα είναι οι Αλγεβρικές Ιδιότητες Γραφημάτων, η οποία περιέχει ορισμούς και αλγεβρικές αλληλεπιδράσεις πάνω στα γραφήματα. Για περισσότερες λεπτομέρειες σχετικά με την άλγεβρα και τη θεωρία γραφημάτων, παραπέμπουμε στα [6], [7] και [29]. Το δεύτερο κεφάλαιο περιέχει τους ορισμούς του Sudoku puzzle και των λατινικών τετραγώνων, τα οποία είναι μια γενίκευση των Sudoku puzzles, όπως θα αναφερθεί παρακάτω. Για εκτενέστερη έρευνα πάνω στα λατινικά τετράγωνα παραπέμπουμε στα [3], [10], [11], [12],[13], [15], [16], [17], [18] και [29]. Στο τρίτο κεφάλαιο απαριθμούνται οι κλάσεις ισοδυναμίας των λατινικών τετραγώνων αρχικά και στη συνέχεια γίνεται απαρίθμηση τριών ειδών Sudoku puzzles, τα οποία είναι τα junior Sudoku puzzles τάξης 44, τα Sudoku puzzles τάξης 9x9 και τα 2-Quasi-μαγικά Sudoku, τα οποία έχουν έναν παραπάνω περιορισμό σε σχέση με τα συνήθη Sudoku. Τέλος, απαριθμούνται οι συμμετρίες των Sudoku puzzles τάξης 9x9 και γίνεται μια σύντομη ανάλυση των μητρώων μετάθεσής τους. Περαιτέρω πληροφορίες βρίσκονται στα [1], [2], [4], [5], [9], [14], [19], [20], [21], [22], και [26]. Στο τέταρτο κεφάλαιο αλλάζει η αυστηρά αλγεβρική προσέγγιση που υπάρχει στις παραπάνω ενότητες. Εδώ παρουσιάζεται το Sudoku puzzle με μια ισοδύναμη μορφή γραφήματος και γίνεται μια σύντομη παρουσίαση βασικών εννοιών της κρυπτογραφίας, καθώς και μια θεωρητική προσέγγιση της κρυπτογράφησης του Sudoku puzzle, με τη βοήθεια του πρωτοκόλλου της μηδενικής γνώσης. Περαιτέρω πληροφορίες βρίσκονται στα [8], [23] και [24]. Στο πέμπτο κεφάλαιο αλλάζει πάλι ο επιστημονικός κλάδος, μέσω του οποίου εξετάζουμε τα Sudoku puzzles και επικεντρώνεται στην απεικόνιση ενός στιγμιοτύπου του puzzle Sudoku σε ένα στιγμιότυπο του προβλήματος SAT. Όλοι οι περιορισμοί του Sudoku θα μπορέσουν να διατηρηθούν μέσω των κανονικών συζευκτικών προτάσεων του προβλήματος SAT, οι οποίες έχουν χωριστεί σε πέντε ενότητες. Η καταμέτρηση των κανονικών συζευκτικών προτάσεων του προβλήματος SAT μέσω αναδρομικών τύπων, αποτελεί το πρωτότυπο τμήμα της διπλωματικής καθώς και η ανάλυση των τύπων αυτών, την οποία περιέχει το επισυναπτόμενο CD. Για πιο θεωρητική προσέγγιση προτείνονται τα [25], [26], [27], [30]. Το έκτο κεφάλαιο της εργασίας περιέχει μια διασκεδαστική εφαρμογή κρυπτογράφησης οποιουδήποτε Sudoku puzzle τάξης 99 . Η εφαρμογή υλοποιείται με τραπουλόχαρτα, έτσι ώστε ο αναγνώστης να είναι σε θέση να κρυπτογραφήσει οποιοδήποτε λύση puzzle Sudoku, χωρίς να είναι υποχρεωμένος να παρουσιάσει τη λύση του στον αντίπαλο, χρησιμοποιώντας μόνο τρείς τράπουλες. Ο στόχος του τελευταίου κεφαλαίου είναι να κάνει τον επίλογο της εργασίας πιο ευχάριστο και πιο ανάλαφρο ακόμα και για νέους επιστήμονες στο χώρο της κρυπτογραφίας, της θεωρίας γραφημάτων και της άλγεβρας.<br>The essay is about the complexity of the Sudoku puzzles and how you can numarated them.
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Books on the topic "Sudoku puzzle"

1

Sudoku Puzzle Book: Sudoku Puzzles. Independently Published, 2022.

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Sudoku Puzzle Book: Sudoku Puzzle Book 200 Puzzles. Independently Published, 2021.

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Medium. Sudoku Puzzle: Sudoku Puzzle Book 1000 Sudoku Puzzles with Solutions. Independently Published, 2021.

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Lopez, Champ. SUDOKU : 500 Sudoku Puzzles: *sudoku puzzle books - master level sudoku puzzle book. Createspace Independent Publishing Platform, 2017.

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Bachari, Abdelaziz, and Sudoku for adults. Sudoku Puzzle: Sudoku Puzzle Book for Adults,hard Sudoku Puzzles,400+sudoku Puzzles Hardest. Independently Published, 2020.

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za, Tapby. Sudoku Puzzle Book : : : Sudoku Puzzles : Easy, Medium, Hard Sudoku Puzzle Book: 500 + Puzzle. Independently Published, 2018.

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Lopez, Champ. SUDOKU : 500*Sudoku Puzzles: *Sudoku Puzzle Books*. Createspace Independent Publishing Platform, 2017.

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1000, sudoku LLC. Sudoku Puzzle Book: Sudoku Puzzle Kids - Sudoku Puzzle Large. Independently Published, 2020.

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Publishing, Puzzle. Sudoku Puzzle Book: 600 Sudoku Puzzles. Independently Published, 2021.

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puzzletreebooks. Sudoku Puzzle Book: 300 Sudoku Puzzles. Independently Published, 2019.

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Book chapters on the topic "Sudoku puzzle"

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Zambon, Giulio. "Puzzle Statistics and More Puzzles." In Sudoku Programming with C. Apress, 2015. http://dx.doi.org/10.1007/978-1-4842-0995-0_16.

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Lenz, Moritz. "Formatting a Sudoku Puzzle." In Raku Fundamentals. Apress, 2020. http://dx.doi.org/10.1007/978-1-4842-6109-5_3.

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Lenz, Moritz. "Formatting a Sudoku Puzzle." In Perl 6 Fundamentals. Apress, 2017. http://dx.doi.org/10.1007/978-1-4842-2899-9_3.

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Zambon, Giulio. "Modeling a Sudoku Puzzle in C." In Sudoku Programming with C. Apress, 2015. http://dx.doi.org/10.1007/978-1-4842-0995-0_1.

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Sudha, V., and R. Kalaiselvi. "The Sudoku Puzzle Generator Using DNA Computing." In Communications in Computer and Information Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-66763-4_1.

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Agarwal, Anshul, Anuradha Tomar, and Venkata Madhava Ram Tatabhatla. "Array Reconfiguration with Arrow Sudoku Puzzle Pattern." In Photovoltaic Partial Shading. CRC Press, 2024. http://dx.doi.org/10.1201/9781003285830-3.

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Huang, Sen, Jin-cai Huang, Qing Chen, Sheng-yun Liu, and Yan-jun Liu. "The Research of Efficient Algorithm to Generate Sudoku Puzzle." In Lecture Notes in Electrical Engineering. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34522-7_77.

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Meng, Jixian, and Xinzhong Lu. "The Design of the Algorithm of Creating Sudoku Puzzle." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21524-7_52.

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Maji, Arnab Kumar, and Rajat Kumar Pal. "A Novel Biometric Template Encryption Scheme Using Sudoku Puzzle." In Advances in Intelligent Systems and Computing. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-1988-0_7.

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Clementis, Ladislav. "Advantage of Parallel Simulated Annealing Optimization by Solving Sudoku Puzzle." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-10783-7_23.

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Conference papers on the topic "Sudoku puzzle"

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Honwade, Rohan, Shanta Rangaswamy, B. R. Roshan Shetty, J. Rohith, and V. Mukund. "Steganography Using Sudoku Puzzle." In 2009 International Conference on Advances in Recent Technologies in Communication and Computing. ARTCom 2009. IEEE, 2009. http://dx.doi.org/10.1109/artcom.2009.116.

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Li, Guo, Xinshe Qi, Na Wang, Ruiping Huang, and Jing Zhao. "Genarate and Solve Sudoku Puzzle." In 2019 10th International Conference on Information Technology in Medicine and Education (ITME). IEEE, 2019. http://dx.doi.org/10.1109/itme.2019.00154.

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Baltaoglu, M. S., B. Onal, and A. E. Pusane. "Sudoku puzzle as an LDPC code." In 2013 21st Signal Processing and Communications Applications Conference (SIU). IEEE, 2013. http://dx.doi.org/10.1109/siu.2013.6531199.

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Shirali-Shahreza, M. Hassan, and Mohammad Shirali-Shahreza. "Steganography in SMS by Sudoku puzzle." In 2008 IEEE/ACS International Conference on Computer Systems and Applications (AICCSA). IEEE, 2008. http://dx.doi.org/10.1109/aiccsa.2008.4493626.

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Howell, Ian, Robert Woodward, Berthe Y. Choueiry, and Christian Bessiere. "Solving Sudoku with Consistency: A Visual and Interactive Approach." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/852.

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We describe an online, interactive system with a graphical interface to illustrate the power and operation of consistency algorithms in a friendly and popular context, namely, solving Sudoku puzzles. Our tool implements algorithms for enforcing five (domain-based) consistency properties on binary and non-binary constraint models. Our tool is useful for research, education, and outreach. From a scientific standpoint, we propose a new consistency property that can solve the hardest known 9×9 Sudoku instances without search, but leave open the question of the lowest level of consistency needed to solve every 9×9 Sudoku puzzle. We have used the current tool and its predecessor in the classroom to introduce students to modeling problems with constraints, explain consistency properties, and illustrate the operations of constraint propagation and lookahead. Finally, we have also used this tool during outreach activities to demystify AI to children and the general public and show them how computers think.
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Vamsi, Kodeti Surya, Sashank Gangadharabhotla, and Vallabhaneni Sri Harsha Sai. "A Deep Learning approach to solve sudoku puzzle." In 2021 5th International Conference on Intelligent Computing and Control Systems (ICICCS). IEEE, 2021. http://dx.doi.org/10.1109/iciccs51141.2021.9432326.

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Moraglio, Alberto, and Julian Togelius. "Geometric particle swarm optimization for the sudoku puzzle." In the 9th annual conference. ACM Press, 2007. http://dx.doi.org/10.1145/1276958.1276975.

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Zou, Yang, Xiaolin Tian, Shaowei Xia, and Yali Song. "A novel image scrambling algorithm based on Sudoku puzzle." In 2011 4th International Congress on Image and Signal Processing (CISP). IEEE, 2011. http://dx.doi.org/10.1109/cisp.2011.6100273.

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Rodríguez-Vázquez, Katya. "GA and entropy objective function for solving sudoku puzzle." In GECCO '18: Genetic and Evolutionary Computation Conference. ACM, 2018. http://dx.doi.org/10.1145/3205651.3208786.

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Ciantar, Keith George, and Owen Casha. "Implementation of a Sudoku Puzzle Solver on a FPGA." In 2023 9th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2023. http://dx.doi.org/10.1109/codit58514.2023.10284457.

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