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A Functional Taxonomy of Logic Puzzles
A Functional Taxonomy of Logic Puzzles Lianne V. Hufkens Cameron Browne Department of Data Science and Knowledge Engineering Maastricht University Maastricht, The Netherlands flianne.hufkens, [email protected] Abstract—There currently exists no taxonomy for the full range of puzzles including “pen & paper” Japanese logic puzzles. We present a functional taxonomy for these puzzles in prepa- ration for implementing them in digital form. This taxonomy reveals similarities and differences between these puzzles and locates them within the context of single player games. Index Terms—games, puzzles, logic, taxonomy, classification I. INTRODUCTION This work is part of a project on digitally implementing the full range of pen & paper puzzles for computer analysis. In order to model these puzzles, it is useful to devise a taxonomy to highlight differences and similarities between Fig. 1: A Sudoku challenge (left) and solution (right). them to facilitate their implementation. We define a puzzle as a problem with defined steps for books, with further examples and information on Nikoli-style achieving one or more defined solutions, such that the chal- logic puzzles obtained from online sources including [2], [3], lenge contains all information needed to achieve its own [4], [5] and [6]. solution. Puzzles are distinct from games as they lack the Some simple schemes for logically grouping logic puzzles adversarial element: ”Puzzles are solved. Games are won.”1 already exist. For example, our final taxonomy was inspired by We focus on the group of puzzles commonly known as the classification found at [2], and Nikoli [3] uses the following Japanese logic puzzles [1], of which Sudoku (Fig. -
Tatamibari Is NP-Complete
Tatamibari is NP-complete The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Adler, Aviv et al. “Tatamibari is NP-complete.” 10th International Conference on Fun with Algorithms, May-June 2021, Favignana Island, Italy, Schloss Dagstuhl and Leibniz Center for Informatics, 2021. © 2021 The Author(s) As Published 10.4230/LIPIcs.FUN.2021.1 Publisher Schloss Dagstuhl, Leibniz Center for Informatics Version Final published version Citable link https://hdl.handle.net/1721.1/129836 Terms of Use Creative Commons Attribution 3.0 unported license Detailed Terms https://creativecommons.org/licenses/by/3.0/ Tatamibari Is NP-Complete Aviv Adler Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Jeffrey Bosboom Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Erik D. Demaine Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Martin L. Demaine Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Quanquan C. Liu Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Jayson Lynch Massachusetts Institute of Technology, Cambridge, MA, USA [email protected] Abstract In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m × n grid of cells, where each cell possibly contains a clue among , , . The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing are square, rectangles containing are strictly longer horizontally than vertically, rectangles containing are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. -
Report to the President: MIT and the Prosecution of Aaron Swartz
Report to the President MIT and the Prosecution of Aaron Swartz Review Panel Harold Abelson Peter A. Diamond Andrew Grosso Douglas W. Pfeiffer (support) July 26, 2013 © Copyright 2013, Massachusetts Institute of Technology This worK is licensed under a Creative Commons Attribution 3.0 Unported License. PRESIDENT REIF’S CHARGE TO HAL ABELSON | iii L. Rafael Reif, President 77 Massachusetts Avenue, Building 3-208 Cambridge, MA 02139-4307 U.S.A. Phone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
THE ART of Puzzle Game Design
THE ART OF Puzzle Design Scott Kim & Alexey Pajitnov with Bob Bates, Gary Rosenzweig, Michael Wyman March 8, 2000 Game Developers Conference These are presentation slides from an all-day tutorial given at the 2000 Game Developers Conference in San Jose, California (www.gdconf.com). After the conference, the slides will be available at www.scottkim.com. Puzzles Part of many games. Adventure, education, action, web But how do you create them? Puzzles are an important part of many computer games. Cartridge-based action puzzle gamse, CD-ROM puzzle anthologies, adventure game, and educational game all need good puzzles. Good News / Bad News Mental challenge Marketable? Nonviolent Dramatic? Easy to program Hard to invent? Growing market Small market? The good news is that puzzles appeal widely to both males and females of all ages. Although the market is small, it is rapidly expanding, as computers become a mass market commodity and the internet shifts computer games toward familiar, quick, easy-to-learn games. Outline MORNING AFTERNOON What is a puzzle? Guest Speakers Examples Exercise Case studies Question & Design process Answer We’ll start by discussing genres of puzzle games. We’ll study some classic puzzle games, and current projects. We’ll cover the eight steps of the puzzle design process. We’ll hear from guest speakers. Finally we’ll do hands-on projects, with time for question and answer. What is a Puzzle? Five ways of defining puzzle games First, let’s map out the basic genres of puzzle games. Scott Kim 1. Definition of “Puzzle” A puzzle is fun and has a right answer. -
Solving Pictorial Jigsaw Puzzle by Stigmergy-Inspired Internet-Based Human Collective Intelligence
Solving Pictorial Jigsaw Puzzle by Stigmergy-inspired Internet-based Human Collective Intelligence Bo Shen Wei Zhang Haiyan Zhao Peking University, Beijing, China Peking University, Beijing, China Peking University, Beijing, China Beijing, China Beijing, China Beijing, China [email protected] [email protected] [email protected] Zhi Jin Yanhong Wu Peking University, Beijing, China Peking University, Beijing, China Beijing, China Beijing, China [email protected] [email protected] ABSTRACT 1 INTRODUCTION The pictorial jigsaw (PJ) puzzle is a well-known leisure game for hu- Pictorial jigsaw (PJ) puzzle is a well-known leisure game for people mans. Usually, a PJ puzzle game is played by one or several human from children to adults. In a PJ puzzle game, the goal is to recover an players face-to-face in the physical space. In this paper, we focus on image with human-sensitive contents from n different pieces of the how to solve PJ puzzles in the cyberspace by a group of physically image, as fast as possible. Besides the appearance of a leisure game, distributed human players. We propose an approach to solving PJ PJ puzzle has a deep metaphorical meaning. It embodies perfectly puzzle by stigmergy-inspired Internet-based human collective intel- a kind of complex problems that can not be resolved in a top-down ligence. The core of the approach is a continuously executing loop, manner, but only in a bottom-up, exploring and growing manner. named the EIF loop, which consists of three activities: exploration, That is, such a problem usually can not be pre-decomposed into a integration, and feedback. -
Algorithmic Combinatorial Game Theory∗
Playing Games with Algorithms: Algorithmic Combinatorial Game Theory∗ Erik D. Demaine† Robert A. Hearn‡ Abstract Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer. 1 Introduction Many classic games are known to be computationally intractable (assuming P 6= NP): one-player puzzles are often NP-complete (as in Minesweeper) or PSPACE-complete (as in Rush Hour), and two-player games are often PSPACE-complete (as in Othello) or EXPTIME-complete (as in Check- ers, Chess, and Go). Surprisingly, many seemingly simple puzzles and games are also hard. Other results are positive, proving that some games can be played optimally in polynomial time. In some cases, particularly with one-player puzzles, the computationally tractable games are still interesting for humans to play. We begin by reviewing some basics of Combinatorial Game Theory in Section 2, which gives tools for designing algorithms, followed by reviewing the relatively new theory of Constraint Logic in Section 3, which gives tools for proving hardness. -
{Download PDF} Mathematical Puzzles of Sam Loyd: Volume 2
MATHEMATICAL PUZZLES OF SAM LOYD: VOLUME 2 PDF, EPUB, EBOOK Sam Loyd,Martin Gardner | 167 pages | 01 Jun 1959 | Dover Publications Inc. | 9780486204987 | English | New York, United States Mathematical Puzzles of Sam Loyd Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Martin Gardner Editor. Bizarre imagination, originality, trickiness, and whimsy characterize puzzles of Sam Loyd, America's greatest puzzler. Present selection from fabulously rare Cyclopedia includes the famous 14—15 puzzles, the Horse of a Different Color, and others in various areas of elementary math. Get A Copy. Paperback , pages. Published June 1st by Dover Publications first published More Details Original Title. Other Editions 6. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Mathematical Puzzles of Sam Loyd , please sign up. Be the first to ask a question about Mathematical Puzzles of Sam Loyd. Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Average rating 3. Rating details. More filters. Sort order. Start your review of Mathematical Puzzles of Sam Loyd. Jan 19, Jennifer rated it it was ok. I'm not all that fond of this style of puzzle. Apr 09, Lindsey Lubker rated it it was amazing Shelves: math. This is a book that has lots of mathematical puzzles. It has easy and tricky parts throughout the book. Mar 07, Julia marked it as to-read. -
By Prof. Mcgonagall Solution to STEPS TOLD: the Grid with The
By Prof. McGonagall weeks belong to a set, such that their an- swers form this meta. Those answers are Solution to STEPS TOLD: reproduced below for your convenience. Thegridwiththewhiteandblackcircles Especially now, without a title or flavor- (ignoring the letters for now) is the Nikoli text to give outright hints, it is important logic puzzle ‘‘Masyu’’. Solving that puzzle to keep in mind Rule 9: Always be on the yieldsapaththroughthegrid. Takingeach lookout for themes and patterns. Para- letteralongthatpathspellstheinstruction graph breaks in a block of text, repeated ‘‘MAKE A CRYPTIC CLUE BY USING THE words or letters, apparent typos or non- REMAINING LETTERS IN ORDER’’. standard word selections -- these all can When read left to right, top to bottom, point to clues. Keep your eyes open, and the unused letters in the grid spell the investigate anything that looks unusual. phrase ‘‘SILLY SEATS RING RED PEERS’’. Enjoy your last day of class, and as This is read as a cryptic crossword clue: always, if you think you have the answer, the definition is ‘‘peers’’, and the wordplay submit it on our website below. tells you to mix up the letters of ‘‘seats’’ We’ll see some of you this Sunday at and place them around the letter ‘R’ (for the Berkeley Mystery Hunt! red). This results in the answer, STARES. The title is another wordplay clue to the METAPUZZLE same answer -- ‘‘told’’ indicates a homo- phone of ‘‘stairs’’, a synonym of ‘‘steps’’. DOTING Congratulations to Jevon Heath and REDUB Melinda Fricke, who first submitted the COLORED correct answer to this puzzle. ONES STARTING This now brings us to the metapuz- REDSTAR zle, a new puzzle consisting solely of the COSTARRED answers to all previous puzzles. -
Integirls Guide to Puzzle Solving
The inteGIRLS Guide to Puzzle Solving Getting Started Strategies Puzzle Anatomy Reading the Puzzle While you're reading the flavor text of the body text of the puzzle, look out for Title Title - Weird words Flavor text: jaksdjfalkdsdf - Name of the puzzle - Awkward phrasing jdfjlkajdfklajdlfkjkfjs;aasdfa - Can be a clue - Things that seem out of place These are almost always part of the solution. Body Flavor text - Full of cryptic clues Look for patterns. Count items and try to - Read and review carefully match the number to other puzzle elements. Body Think about multiple approaches, including - Substance of the puzzle the obvious ones - With the internet, this is everything you need Use the internet to your advantage. If you get stuck on a puzzle, ask a teammate Finishing a Puzzle to look over the puzzle, or take a break. Direct Answer Methods Cryptic phrase Collaborate! - Index into words (look at Sometimes, puzzles Mechanics for more info) end with a phrase. - Change from a cipher to letters This can be... Solution - Look for missing letters, extra letters, or changed letters - A clue or riddle to Every puzzle answer is a Examples - Letters are images drawn in the the final answer word or phrase in English - Kermit the puzzle - Instructions on how Frog - Eliminate letters that are not part to use elements in the Every element of the - Zimbabwe of the puzzle or isolate indicated puzzle to find the final puzzle is involved in getting - Hydrogen letters answer the answer The inteGIRLS Guide to Puzzle Solving Some Mechanics Tools - Anagramming -
Happy Holidays from the Solechen Family
Happy Holidays from the SoleChen Family 201<3 Reasons to be Happy! J Seattle sightseeing Jasper here! The big news is that Lady Grey found a home this summer. We A surprise trip for D N are all very happy for her! I am happy for the male human; his ignite-thing speech—while about music and not cats—was popular anyway. Also I am F JoCo Cruise trip E now an older cat who takes pills every day so I don’t limp. I’m happy the Oscar Party B humans figured that out before I bit Tye too much! M GC Summit A @DeeAnnSole Int’l Tabletop Day Pleasant Surprises R In January, Curtis surprised DeeAnn with a post-birthday trip; in July, A “100 Rejections” party DeeAnn began lying to Curtis—so dozens of people could create a secret, P Paradise Lost Star Trek-themed puzzle hunt just for him. “The Double Secret Game” and R Curtis’ 40th birthday party were a HUGE success. DeeAnn also helped M Portland Afoot Game with several other puzzle hunts, was point person for OryCon 35’s A WhiskeyFest NW Guests of Honor, attended the first two weddings she’s cried at, and Y DASH 5 PDX played lots and lots of great games. DeeAnn is now working part-time for Sauvie Island a new startup she believes could revolutionize mental healthcare. J D+Mom road trip U Open Source Bridge N @sparCKL WarTron Boston Words Do Not Fail @CurtisCChen J Readercon Imagine Curtis’ surprise when Janet “Query Shark” Reid called his query U JayWake letter for Waypoint Kangaroo “a Win on the First Try” and asked to see L Puzzled Pint turns 3 the full manuscript! (She provided excellent rewrite notes.) Curtis also Mt. -
Baguenaudier - Wikipedia, the Free Encyclopedia
Baguenaudier - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Baguenaudier You can support Wikipedia by making a tax-deductible donation. Baguenaudier From Wikipedia, the free encyclopedia Baguenaudier (also known as the Chinese Rings, Cardan's Suspension, or five pillars puzzle) is a mechanical puzzle featuring a double loop of string which must be disentangled from a sequence of rings on interlinked pillars. The puzzle is thought to have been invented originally in China. Stewart Culin provided that it was invented by the Chinese general Zhuge Liang in the 2nd century AD. The name "Baguenaudier", however, is French. In fact, the earliest description of the puzzle in Chinese history was written by Yang Shen, a scholar in 16th century in his Dan Qian Zong Lu (Preface to General Collections of Studies on Lead). Édouard Lucas, the inventor of the Tower of Hanoi puzzle, was known to have come up with an elegant solution which used binary and Gray codes, in the same way that his puzzle can be solved. Variations of the include The Devil's Staircase, Devil's Halo and the Impossible Staircase. Another similar puzzle is the Giant's Causeway which uses a separate pillar with an embedded ring. See also Disentanglement puzzle Towers of Hanoi External links A software solution in wiki source (http://en.wikisource.org/wiki/Baguenaudier) Eric W. Weisstein, Baguenaudier at MathWorld. The Devil's Halo listing at the Puzzle Museum (http://www.puzzlemuseum.com/month/picm05/200501d-halo.htm) David Darling - encyclopedia (http://www.daviddarling.info/encyclopedia/C/Chinese_rings.html) Retrieved from "http://en.wikipedia.org/wiki/Baguenaudier" Categories: Chinese ancient games | Mechanical puzzles | Toys | China stubs This page was last modified on 7 July 2008, at 11:50. -
Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity∗
Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity∗ Erik D. Demaine, Martin L. Demaine MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA, {edemaine,mdemaine}@mit.edu Dedicated to Jin Akiyama in honor of his 60th birthday. Abstract. We show that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete. Furthermore, we show direct equivalences between these three types of puzzles: any puzzle of one type can be converted into an equivalent puzzle of any other type. 1. Introduction Jigsaw puzzles [37,38] are perhaps the most popular form of puzzle. The original jigsaw puzzles of the 1760s were cut from wood sheets using a hand woodworking tool called a jig saw, which is where the puzzles get their name. The images on the puzzles were European maps, and the jigsaw puzzles were used as educational toys, an idea still used in some schools today. Handmade wooden jigsaw puzzles for adults took off around 1900. Today, jigsaw puzzles are usually cut from cardboard with a die, a technology that became practical in the 1930s. Nonetheless, true addicts can still find craftsmen who hand-make wooden jigsaw puzzles. Most jigsaw puzzles have a guiding image and each side of a piece has only one “mate”, although a few harder variations have blank pieces and/or pieces with ambiguous mates. Edge-matching puzzles [21] are another popular puzzle with a similar spirit to jigsaw puzzles, first appearing in the 1890s. In an edge-matching puzzle, the goal is to arrange a given collection of several identically shaped but differently patterned tiles (typically squares) so that the patterns match up along the edges of adjacent tiles.