Transreality Puzzle As New Genres of Entertainment Technology
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Dill's Greenhouse Tour
DILL’S GREENHOUSE TOUR: The Dill’s Greenhouse Tour includes the Columbus Park of Roses in Whetstone Park, Dill’s Greenhouse, Gantz Farm, and the International Harvest Garden. Come smell the roses, learn about herbs, and even go on a hayride. Columbus Park of Roses at Whetstone Park This 13-acre park contains three unique rose gardens, an Earth-Kind® Rose Garden, Main Rose Garden and Heritage Garden as well as herb and perennial gardens. One of the largest public rose gardens in the United States, the Park of Roses in Whetstone Park has been among the most beautiful places in Columbus since 1953. It has grown to include 12,000 roses of more than 400 varieties. The park is a certified arboretum and ranked among the top 10 public rose gardens in the country by the All-American Rose Selections. (parkofroses.org) . Dill’s Greenhouse Dill’s Greenhouse is a local, family-owned business started in 1983. They have a knowledgeable team eager to share their love of gardening. They grow their own annuals, perennials, vegetable plants and hanging baskets. Nearly all the nursery stock is Ohio-grown increasing the success rate of its trees and shrubs. Our Tour will coincide with their annual Fall Fun Festival featuring a 5-acre corn maze, an indoor straw maze and (weather permitting) a hayride given by owner Jerry Dill. At Dill’s, “Only Nature Does It Better.” (dillsgreenhouse.net) . The Gardens at Gantz Farm After being a “hidden gem” of Grove City and the greater Columbus area for 26 years, The Garden at Gantz Farm is ready to take it’s spot in the limelight. -
Math Games: Sliding Block Puzzles 09/17/2007 12:22 AM
Math Games: Sliding Block Puzzles 09/17/2007 12:22 AM Search MAA Membership Publications Professional Development Meetings Organization Competitions Math Games sliding-block Puzzles Ed Pegg Jr., December 13, 2004 The December issue of The Economist contains an article with a prominent question. Has an inventor found the hardest possible simple sliding-block puzzle? It goes on to describe the Quzzle puzzle, by Jim Lewis. The article finishes with "Mr Lewis claims that Quzzle, as he dubs his invention, is 'the world's hardest simple sliding-block puzzle.' Within the terms of his particular definition of 'simple,' he would seem to have succeeded." The claim is wrong. Quzzle is not the world's hardest simple sliding-block puzzle, no matter how you define "hard." Sometimes, hard means lot and lots of moves. Junk Kato has succinctly described a record setting series for the most moves required with n pieces. The basic underlying principle is Edouard Lucas' Tower of Hanoi puzzle. Move the red piece to the bottom slot. Figure 1. Junk's Hanoi by Junk Kato. From Modern sliding-block Puzzles. Often, "hard" maximizes complexity with a sparse number of pieces. Usually, the fewer the pieces, the better the puzzle. Two people at the forefront of making really hard sliding-block puzzles with just a few pieces are Oskar van Deventer and James Stephens. James started with Sliding-Block Puzzles. The two of them collaborated to create the ConSlide Puzzle and the Bulbous Blob Puzzle. Oskar even went so far as to make a prototype of the excellent Simplicity puzzle. -
English Turf Labyrinths Jeff Saward
English Turf Labyrinths Jeff Saward Turf labyrinths, or ‘turf mazes’ as they are popularly known in Britain, were once found throughout the British Isles (including a few examples in Wales, Scotland and Ireland), the old Germanic Empire (including modern Poland and the Czech Republic), Denmark (if the frequently encountered Trojaborg place-names are a reliable indicator) and southern Sweden. They are formed by cutting away the ground surface to leave turf ridges and shallow trenches, the convoluted pattern of which produces a single pathway, which leads to the centre of the design. Most were between 30 and 60 feet (9-18 metres) in diameter and usually circular, although square and other polygonal examples are known. The designs employed are a curious mixture of ancient classical types, found throughout the region, and the medieval types, found principally in England. Folklore and the scant contemporary records that survive suggest that they were once a popular feature of village fairs and other festivities. Many are found on village greens or commons, often near churches, but sometimes they are sited on hilltops and at other remote locations. By nature of their living medium, they soon become overgrown and lost if regular repair and re-cutting is not carried out, and in many towns and villages this was performed at regular intervals, often in connection with fairs or religious festivals. 50 or so examples are documented, and several hundred sites have been postulated from place-name evidence, but only eleven historic examples survive – eight in England and three in Germany – although recent replicas of former examples, at nearby locations, have been created at Kaufbeuren in Germany (2002) and Comberton in England (2007) for example. -
11 Triple Loyd
TTHHEE PPUUZZZZLLIINNGG SSIIDDEE OOFF CCHHEESSSS Jeff Coakley TRIPLE LOYDS: BLACK PIECES number 11 September 22, 2012 The “triple loyd” is a puzzle that appears every few weeks on The Puzzling Side of Chess. It is named after Sam Loyd, the American chess composer who published the prototype in 1866. In this column, we feature positions that include black pieces. A triple loyd is three puzzles in one. In each part, your task is to place the black king on the board.to achieve a certain goal. Triple Loyd 07 w________w áKdwdwdwd] àdwdwdwdw] ßwdwdw$wd] ÞdwdRdwdw] Ýwdwdwdwd] Üdwdwdwdw] Ûwdwdpdwd] Údwdwdwdw] wÁÂÃÄÅÆÇÈw Place the black king on the board so that: A. Black is in checkmate. B. Black is in stalemate. C. White has a mate in 1. For triple loyds 1-6 and additional information on Sam Loyd, see columns 1 and 5 in the archives. As you probably noticed from the first puzzle, finding the stalemate (part B) can be easy if Black has any mobile pieces. The black king must be placed to take away their moves. Triple Loyd 08 w________w áwdwdBdwd] àdwdRdwdw] ßwdwdwdwd] Þdwdwdwdw] Ýwdw0Ndwd] ÜdwdPhwdw] ÛwdwGwdwd] Údwdw$wdK] wÁÂÃÄÅÆÇÈw Place the black king on the board so that: A. Black is in checkmate. B. Black is in stalemate. C. White has a mate in 1. The next triple loyd sets a record of sorts. It contains thirty-one pieces. Only the black king is missing. Triple Loyd 09 w________w árhbdwdwH] àgpdpdw0w] ßqdp!w0B0] Þ0ndw0PdN] ÝPdw4Pdwd] ÜdRdPdwdP] Ûw)PdwGPd] ÚdwdwIwdR] wÁÂÃÄÅÆÇÈw Place the black king on the board so that: A. -
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. -
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. -
Klondike (Sam Loyd)
Back From The Klondike by Sam Loyd The original puzzle was in black and white and had 1 challange: Start from that heart in the center and go three steps in a straight line in any one of the eight directions, north, south, east or west, or northeast, northwest, southeast or southwest. When you have gone three steps in a straight line, you will reach a square with a number on it, which indicates the second day's journey, as many steps as it tells, in a straight line in any of the eight directions. From this new point when reached, march on again according to the number indicated, and continue on, following the requirements of the numbers reached, until you come upon a square with a number which will carry you just one step beyond the border, when you are supposed to be out of the woods and can holler all you want, as you will have solved the puzzle. Joseph Eitel!Page 1 of 6!amagicclassroom.com Back From the Klondike Version 2 This maze was among the many puzzles Loyd created for newspapers beginning in 1890. In this version some squares are yellow or green. This allowed better explanations how the puzzle worked. The numbers in each square in the grid indicate how many squares you can travel in a straight line horizontally, vertically, or diagonally from that square. For example, if you start in the red square in the center, your first move can take you to any one of the three yellow squares. The green squares are some of the possible squares you could land on for the second move. -
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. -
Lagrange 1 of 22 the Great Mathematical Puzzelist Samuel Loyd Was Born in Philadelphia, Pennsylvania in 1841 (O'conner). He Wa
LaGrange 1 of 22 The great mathematical puzzelist Samuel Loyd was born in Philadelphia, Pennsylvania ’Conner). He was the youngest of nine children. At the age of three, his family moved in 1841 (O to New York where he attended public school (Carter). Sam Loyd got his start in the puzzle business with chess. At 14 years of age, Loyd started attending chess club with two of his older “New brothers. On April 14th, that same year, Loyd had his first chess problem published in the ” In 1856, the “New York Clipper” published another of his chess York Saturday Courier. ’Conner). At first, all of Loyd’s puzzles were hobbies. problems for which he won a prize (O After school he studied engineering and earned a license in steam and mechanical engineering (Loyd). For a time, Loyd supported himself as a plumbing contractor and the owner of a chain of ’Conner). Plus, music stores. He was also a skilled cartoonist and a self taught wood engraver (O he was skilled in conjuring, mimicry, ventriloquism and silhouette cutting (Gardner). Eventually, Loyd left plumbing behind and focused on mathematical puzzles. He attended chess tournaments, wrote and edited mechanical journals along with his magazine “Sam Loyd’s Puzzle Magazine” (O’Conner). For a while, he also edited the magazine entitled “Chess Monthly” and the chess page of “Scientific American” (Gardner). P. T. Barnum’s Trick ’Conner). This sale alone Donkey was invented by Sam Loyd and sold to Barnum in 1870 (O grossed $10,000 for Loyd (Carter). In 1878 Loyd published his one and only hard cover book Chess Strategy, which included all the chess problems published in Scientific American plus ’Conner). -
Amusements in Mathematics, by Henry Ernest Dudeney
Transcribers note: Many of the puzzles in this book assume a familiarity with the currency of Great Britain in the early 1900s. As this is likely not common knowledge for those outside Britain (and possibly many within,) I am including a chart of relative values. The most common units used were: the Penny, abbreviated: d. (from the Roman penny, denarius) the Shilling, abbreviated: s. the Pound, abbreviated: £ There was 12 Pennies to a Shilling and 20 Shillings to a Pound, so there was 240 Pennies in a Pound. To further complicate things, there were many coins which were various fractional values of Pennies, Shillings or Pounds. Farthing ¼d. Half-penny ½d. Penny 1d. Three-penny 3d. Sixpence (or tanner) 6d. Shilling (or bob) 1s. Florin or two shilling piece 2s. Half-crown (or half-dollar) 2s. 6d. Double-florin 4s. Crown (or dollar) 5s. Half-Sovereign 10s. Sovereign (or Pound) £1 or 20s. This is by no means a comprehensive list, but it should be adequate to solve the puzzles in this book. AMUSEMENTS IN MATHEMATICS by HENRY ERNEST DUDENEY In Mathematicks he was greater Than Tycho Brahe or Erra Pater: For he, by geometrick scale, Could take the size of pots of ale; Resolve, by sines and tangents, straight, If bread or butter wanted weight; And wisely tell what hour o' th' day The clock does strike by algebra. BUTLER'S Hudibras . 1917 PREFACE Pg v In issuing this volume of my Mathematical Puzzles, of which some have appeared in periodicals and others are given here for the first time, I must acknowledge the encouragement that I have received from many unknown correspondents, at home and abroad, who have expressed a desire to have the problems in a collected form, with some of the solutions given at greater length than is possible in magazines and newspapers. -
L-G-0003950258-0013322245.Pdf
The Tower of Hanoi – Myths and Maths Andreas M. Hinz • Sandi Klavzˇar Uroš Milutinovic´ • Ciril Petr The Tower of Hanoi – Myths and Maths Foreword by Ian Stewart Andreas M. Hinz Uroš Milutinovic´ Faculty of Mathematics, Faculty of Natural Sciences Computer Science and Statistics and Mathematics LMU München University of Maribor Munich Maribor Germany Slovenia Sandi Klavzˇar Ciril Petr Faculty of Mathematics and Physics Faculty of Natural Sciences University of Ljubljana and Mathematics Ljubljana University of Maribor Slovenia Maribor Slovenia and Faculty of Natural Sciences and Mathematics University of Maribor Maribor Slovenia ISBN 978-3-0348-0236-9 ISBN 978-3-0348-0237-6 (eBook) DOI 10.1007/978-3-0348-0237-6 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012952018 Mathematics Subject Classification: 00-02, 01A99, 05-03, 05A99, 05Cxx, 05E18, 11Bxx, 11K55, 11Y55, 20B25, 28A80, 54E35, 68Q25, 68R05, 68T20, 91A46, 91E10, 94B25, 97A20 Ó Springer Basel 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer.