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The discussion covers n-queens, Sudoku generation and solving, Einstein riddle logic puzzles, 15-puzzle, maximum clique, and Graeco-Latin squares, supported by explanations of required Boolean logic concepts.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/eective-problem-solving-using-sat-solvers/267115/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/eective-problem-solving-using-sat-solvers/267115.png","ImageObject",300,407,{"name":42,"@type":43},"Aran","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-08","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the SAT problem described in the article?","Question",{"text":63,"@type":64},"The SAT problem determines whether a given Boolean expression can be satisfied by assigning true/false values to its variables so the entire formula becomes true.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does Maple’s Satisfy command help solve encoded problems?",{"text":68,"@type":64},"Satisfy returns a satisfying assignment for a Boolean expression when one exists; it returns NULL when no satisfying assignment exists.",{"name":70,"@type":61,"acceptedAnswer":71},"Which kinds of puzzles and problems does the article show how to solve with SAT solvers?",{"text":72,"@type":64},"It demonstrates SAT-based solutions for n-queens, Sudoku, logic puzzles like the Einstein riddle, the 15-puzzle, the maximum clique problem, and finding Graeco-Latin squares.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267115,1790436305,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":55,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","E􀀋ective problem solving using SAT solvers  \nCurtis Bright 1 ;2 , J􀁿urgen Gerhard2 , Ilias Kotsireas3 , and Vijay Ganesh 1  \n1 University of Waterloo, Waterloo, Canada  \n2 Maplesoft, Waterloo, Canada  \n3 Wilfrid Laurier University, Waterloo, Canada  \nAbstract. In this article we demonstrate how to solve a variety of problems and puzzles using the built-in SAT solver of the computer algebra system Maple. Once the problems have been encoded into Boolean logic, solutions can be found (or shown to not exist) automatically, without the need to implement any search algorithm. In particular, we describe how to solve the n-queens problem, how to generate and solve Sudoku puzzles, how to solve logic puzzles like the Einstein riddle, how to solve the 15-puzzle, how to solve the maximum clique problem, and 􀀌nding Graeco-Latin squares.  \nKeywords: SAT solving 􀀁 Maple 􀀁 n-queens problem 􀀁 Sudoku 􀀁 Logic puzzles 􀀁 15-puzzle 􀀁 Maximum clique problem 􀀁 Graeco-Latin squares  \n1 Introduction  \n\\ . . . it is a constant source of annoyance when you come up with a clever special algorithm which then gets beaten by translation to SAT.\"  \n|Chris Je􀀋erson  \nThe satis􀀌ability (SAT) problem is to determine if a given Boolean expression can be satis􀀌ed|is there some way of assigning true and false to its variables that makes the whole formula true? Despite at 􀀌rst seeming disconnected from most of the kinds of problems that mathematicians care about we argue in this paper that it is in the interests of mathematicians to have a familiarity with SAT solving and encoding problems in SAT. An immense amount of e􀀋ort over the past several decades has produced SAT solvers that are not only practical for many problems but are actually the fastest known way of solving an impressive variety of problems such as software and hardware veri􀀌cation problems [3] . They have also recently been used to resolve long-standing mathematical conjectures [12] and construct large combinatorial designs [7] .  \nSince 2018, the computer algebra system Maple has included the awardwinning SAT solver MapleSAT [15] as its built-in SAT solver. This solver can be used through the Satisfy command of the Logic package. Satisfy returns a satisfying assignment of a given Boolean expression (if one exists) or NULL if no satisfying assignment exists. In this paper we demonstrate through a number of detailed examples how Satisfy can be an e􀀋ective and e􀀎cient way of solving a variety of problems and puzzles.  \n2 C. Bright, J. Gerhard, I. Kotsireas, V. Ganesh  \nVery little prerequisites are necessary to understand this paper; the main necessary background is a familiarity with Boolean logic which we outline in Section 2 . We then present e􀀋ective solutions to the n-queens problem (Section 3), logic puzzles like the Einstein riddle (Section 4), Sudoku puzzles (Section 5), Euler's Graeco-Latin square problem (Section 6), the maximum clique problem (Section 7), and the 15-puzzle (Section 8) . In each case we require no knowledge of any of the special-purpose search algorithms that have been proposed to solve these problems; once the problems have been encoded into Boolean logic they are automatically solved using Maple's Satisfy.  \nAll of the examples discussed in this paper were implemented and run in Maple 2018 and Maple 2019 . Due to space constraints we have not included our code in this paper, but Maple worksheets containing complete implementations have been made available online through the Maple Application Center [6] .  \n2 Background  \nA basic understanding of Boolean logic is the only prerequisite necessary to understand the solutions described in this paper. One of the main advantages of Boolean logic (but also one of its main disadvantages) is its simplicity: each variable can assume only one of two values denoted by true and false. Boolean expressions consist of variables joined by Boolean operators. The most common Boolean operators (and the ones available in the Logic package of Map","cbCaii8vCNhpgd3n","https://ap.wps.com/l/cbCaii8vCNhpgd3n","pdf",413633,15,"English","# Introduction\n## SAT solving with MapleSAT\n# Background\n## Boolean logic prerequisites\n## Operators and normal form (CNF)","[{\"question\":\"What is the SAT problem described in the article?\",\"answer\":\"The SAT problem determines whether a given Boolean expression can be satisfied by assigning true/false values to its variables so the entire formula becomes true.\"},{\"question\":\"How does Maple’s Satisfy command help solve encoded problems?\",\"answer\":\"Satisfy returns a satisfying assignment for a Boolean expression when one exists; it returns NULL when no satisfying assignment exists.\"},{\"question\":\"Which kinds of puzzles and problems does the article show how to solve with SAT solvers?\",\"answer\":\"It demonstrates SAT-based solutions for n-queens, Sudoku, logic puzzles like the Einstein riddle, the 15-puzzle, the maximum clique problem, and finding Graeco-Latin squares.\"}]","E􀀋ective problem solving using SAT solvers | PDF",1789414910,38]