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Topic: Sprouts (game)

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	Sprouts (game) - Wikipedia, the free encyclopedia
		Sprouts is a pencil-and-paper game with interesting mathematical properties.
		Despite this, the game is finite, and indeed the total number of moves is predetermined by the initial number of crosses: the players cannot affect the result by their play.
		The Game of Sprouts at University of Utah (with an interactive applet).
	en.wikipedia.org /wiki/Sprouts_(game) (852 words)

	Sprouts
		Sprouts is played by two players, starting with a few dots (called spots) drawn on a sheet of paper.
		Sprouts has been studied from the perspectives of graph theory and of topology.
		Sprouts featured in the plot of the first part of the science fiction novel Macroscope by Piers Anthony.
	www.daviddarling.info /encyclopedia/S/Sprouts.html (318 words)

	Wario Ware, Inc: Mega Microgame$ Pyoro FAQ - IGN FAQs
		It isn't long before the sprouts are almost raining down on the poor bird-thing, and movement becomes difficult between threatening sprouts and missing sections of ground.
		Those cases aren't always hopeless, since red sprouts are not rare and flashing ones show up with ever-greater frequency as points are scored, but it often is. The higher up on the screen a sprout is when Pyoro's tongue grabs it the more points it's worth.
		When such a sprout is caught, it not only scores the typical points depending on its height on the screen but it also earns 50 for every sprout on the screen.
	faqs.ign.com /articles/431/431484p1.html (1481 words)

	Science News Online - Ivars Peterson's MathLand - 4/5/97
		Hence, their prediction for a game involving twelve dots is a win for the second player (remainder is zero after dividing twelve by six).
		Sprouts was invented in 1967 by Princeton mathematician John H. Conway and by Michael S. Paterson, when both were at the University of Cambridge in England.
		"Sprouts is an intellectual game that has had an underground popularity with scientists for a number of years," one character in the novel notes.
	www.sciencenews.org /sn_arc97/4_5_97/mathland.htm (820 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Here are the elements of Sprouts notation I have developed in response to the discussion earlier this month under the "Game of Sprouts" topic in geometry-research.
		Element 1: Basic position notation In an N-spot Sprouts game, the initial N spots are numbered 1,2,...,N and the spots added in the course of the game are numbered starting at N+1.
		It is possible to specify a move in Sprouts by providing the full position after the move--in fact, the full position notation provides a complete history of a game.
	www.ics.uci.edu /~eppstein/cgt/sprouts.html (1499 words)

	Guide to Math Night
		Sprouts starts with three (or more) dots on a piece of paper.
		Notice in the animated game that there are two dots that are not used-up at the end.
		This game is a good tool for building your sense of spatial perception on flat surfaces.
	orion.math.iastate.edu /mathnight/activities/other/ppg/sprouts.shtml (259 words)

	Sprouts: Analyzing a Simple Game
		A very simple game which has its origins in the field of Discrete Mathematics is a game called Sprouts.
		Since one arc is lost for each move, the maximum number of moves in a 2-dot game is 5.
		To be certain that you understand the game, determine in each of the following cases whether the game situation could occur.
	staff.imsa.edu /math/journal/volume2/webver/sprouts.html (702 words)

	Joseph Malkevitch: Tidbits: Sprouts (Site not responding. Last check: 2007-10-13)
		Sprouts is a delightful geometrical game invented by John Horton Conway and Michael Paterson February 21, 1967!
		At the start of the game the value of the position is 3n where n is the number of dots.
		Brussel Sprouts is similar to sprouts but starts with n small crosses instead of n dots.
	www.york.cuny.edu /~malk/tidbits/tidbit-sprouts.html (616 words)

	nrich.maths.org::Mathematics Enrichment::Sprouts
		The game is simple enough for younger children to understand, and has also provided experienced mathematicians with significant food for thought.
		The game of Sprouts was invented in 1967 by two mathematicians John H. Conway and Michael S. Paterson, when they were both at the University of Cambridge in the UK.
		The game was popularised by one of Martin Gardner's "Mathematical Games" columns in Scientific American.
	nrich.maths.org /public/viewer.php?obj_id=2413&part=index&refpage=monthindex.php (1478 words)

	Impartial game - Wikipedia, the free encyclopedia
		In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric.
		Impartial games can be analyzed using Sprague-Grundy theory.
		A game that is not impartial is called a partisan game.
	en.wikipedia.org /wiki/Impartial_game (128 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		In the normal game, the last person to move is the winner.
		It turns out that live spots at the end of the game are the key to making the game fun to play.
		Sprouts was invented in 1967 by two extraordinary mathematicians, John H. Conway and Michael S. Paterson.
	www.geocities.com /chessdp/rules.htm (449 words)

	[No title]
		Impartial games Some of the games discussed have the property that the set of moves available in a position are not dependent on whose move it is, and the winner is the one who makes the last move.
		That is, that the nimber of the join of two games is just a function of the nimbers of the two parts.
		In general in a game A, it will be possible to make moves whose nimber is any nimber less than [A], but it will also in general be possible to make moves that have nimbers greater than [A].
	www.cs.cmu.edu /afs/cs/academic/class/15859-f01/www/notes/sleator-nim-notes.txt (1214 words)

	Online Mind Games,Sprouts,Board Games : ... (Site not responding. Last check: 2007-10-13)
		The game is confined only by the playing surface, so for a short game, play within a box drawn on a piece of paper; for a longer game with many players, use a sheet of newsprint.
		Draw a box around the dots to set the limits of the game, or let the edges of the paper be the boundaries.
		(In the illustrated game, the solid dots were drawn on the page to begin the game; the open circles indicate the halfway points of the lines the players drew).
	www.4to40.com /4to40.com_non_ssl/games/4mind/index.asp?article=games_4mind_sprouts (386 words)

	Brussels Sprouts - A Pencil And Paper Game
		Sprouts is a pencil and paper game designed in 1967 by John H. and by Michael S. Paterson.
		Although this game appears to be quite similar to the game of Sprouts, there is an interesting difference.
		In Sprouts, the number of available "dots" is always decreasing because each line uses two dots while creating only one.
	articlesforeducators.com /dir/games/strategy_games/brussels_sprouts.asp (420 words)

	Ivars Peterson's MathLand
		The game of sprouts has a way of growing on you.
		The game has also attracted the attention of mathematicians, who have investigated the game in terms of graph theory and topology.
		Sprouts was invented in 1967 by Princeton mathematician John H. Conway and Michael S. Paterson, when both Conway and Paterson were at the University of Cambridge in England.
	www.maa.org /mathland/mathland_4_7.html (799 words)

	Open Directory - Games:Paper and Pencil (Site not responding. Last check: 2007-10-13)
		Games played by making marks on paper, whether these are symbols, numbers, or drawings, such as Tic Tac Toe, Dots and Boxes, Hangman, Sprouts, Battleship, or Nim.
		Occasionally Board Game variants of the pencil and paper game are published, where the basic elements are pre-formed or preprinted.
		Sprouts is a topological pencil-and-paper game invented in 1967 by mathematician John Horton Conway (who also designed the computer game "Life") and Michael S. Paterson, both of the University of Cambridge in the United Kingdom.
	dmoz.org /Games/Paper_and_Pencil/desc.html (207 words)

	Northwest Indiana News: nwitimes.com
		Pungent, woodsy mushrooms are redolent with the aroma of the earth preparing for a long winter's nap, and dining tables are itching to be laden with the glory of game.
		Panos was introduced to cooking game as an intern for chef Jean-Claude Poilevey at Chicago's La Fontaine (now closed), while a student in the Kendall College culinary program.
		And whether it's wild game or conventional meat, he says to apply the same cooking method of marinating and braising tough cuts and barely threatening the tender ones.
	nwitimes.com /site_pages/panos.php (2193 words)

	Socratic Tutorial 2
		She wants to keep an even number of cannibals, signifying that she did not move last, since every move changes the parity of the number of cannibals.
		A trap is a configuration which if played as a game is won by the person moving second, both in normal and misere play.
		Sprouts positions are continually evolving in the direction of UTs.
	www.geocities.com /chessdp/soctut2.htm (836 words)

	USTINET Open Diectory Search (Site not responding. Last check: 2007-10-13)
		Word game to help improve memory, requires only a pencil and a sheet of paper.
		Games to play on paper, during a boring lecture.
		Game where players take the role of wizards battling it out in an arena.
	news.usti.net /home/search/od/dir.cgi?d=/Games/Paper_and_Pencil (248 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Prove that the number of moves in a game of Brussel Sprouts is a function of n.
		In the set representation of a sprouts position there is a set of regions, and each of these is a set of boundaries.
		Compute the grundy number of the sprouts position that consists of 3 spots connected by a line.
	www.cs.cmu.edu /afs/cs/academic/class/15859-f01/www/homework/assignment2.html (352 words)

	Pencil and Paper Games
		Pipelayer is a game played with two grids of dots that are slightly offset from one another, as shown in the animation at the right.
		The blue player wins the example game and then his connecting path from left to right lights up yellow.
		Capture is a two player game played on a grid of dots like the one shown in the animation to the right.
	orion.math.iastate.edu /danwell/MathNight/ppg.html (628 words)

	David Molnar's Sprouts page (Site not responding. Last check: 2007-10-13)
		The game cannot end with any dots that have more than one life left, because such a dot can be connected to itself, so the total number of turns will be 3n minus the number of live spots remaining.
		The game can be lengthened by producing pharisees, which are dead dots with only dead neighbors, and therein lies the control.
		In the 2002 games tournament, we will be playing Sprouts on a torus, which is what mathematicians call the surface of a donut.
	www.stolaf.edu /people/molnar/games/sprouts (552 words)

	KidSprout Jumboree
		For example, a SproutMeister trying to avoid leading the "Craft Time!" Activity might claim that she is allergic to yarn, while one trying to avoid leading the "Pitching a Pup Tent" Activity might claim that he suffers from medorthophobia.
		For example, if the player's Schedule shows they led an activity for four hours with Sprouts worth 1, 2, 3, and 5 (a total of 11), the Stress Point value of this Activity would be 4 x 11, or 44.
		Playing Excuses on your own Sprouts to subtract from their values when you are in danger of leading an Activity is often a good tactic, but it might be better to play an Excuse on another player's Sprout, and add to its value.
	www.ludism.org /piecepack/jumboree.html (1913 words)

	Brussels sprouts: surprise! They're good - Slashfood
		I also did not like brussel sprouts growing up due to their bitter taste, but I was always served frozen brussel sprouts and fresh brussel sprouts are quite sweet in flavor, especially when braised.
		Brussel sprouts are one of my favorite vegetables.They have been given a bad rep.I tried this out on a chef friend of mine and changed her perspective.In a slow cooker, a pound or more of frozen brussel sprouts.Either ham hocks or lean turkey sausage.Lots of garlic,fresh ginger,and red pepper flakes(optional),olive oil,and lemon juice(optional).4-6 hrs.Mmmm good.
		That initial bitterness was softened by the tender sprout, and the mixed butter and garlic sauce.
	www.slashfood.com /2005/10/26/brussels-sprouts-surprise-theyre-good (1483 words)

	Mathematical game [encyclopedia] (Site not responding. Last check: 2007-10-13)
		Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics.
		Mathematical Games was the title of a long-running column on the subject by Martin Gardner in Scientific American.
		Game theory has wide social and military applications for tactical and strategic planning.
	www.kosmoi.com /Science/Mathematics/Games (219 words)

	Combinatorial Game Theory (Site not responding. Last check: 2007-10-13)
		Joust, a game in which two knights use up the squares of a chessboard until one is stuck.
		In this game, a position is represented by a number, and one moves by either adding or subtracting the largest prime number less than or equal to the position.
		Sprouts, a game invented by Conway and Paterson in which players construct a degree-three planar graph by drawing two-edge ears.
	www.ics.uci.edu /~eppstein/cgt (1499 words)

	[No title]
		One variation of Wythoff's Game, slightly easier to analyze, is to restrict the number of beans taken from a pile on any one turn to let's say three.
		Nim is the granddaddy of impartial games, and if you have spent too much time on-line you may have seen this as the "fruit game".
		In the game of Kayles, n bowling pins are arranged in a row.
	www.stolaf.edu /people/molnar/ps/problems_games.html (1648 words)

	Sprouts - A Two Player Game
		Reactions to the game vary depending on the personality of the player; some treat it as a game of luck (which it is not) and will play it again and again with the same abandon as they might play the card game 'War'.
		This may be a number anywhere from five on up - but keep in mind that the length of the game increases with the number of dots on the paper.
		After playing a few games, it will become evident that the number of dots, as well as who goes first, plays a significant role in who wins.
	www.articlesforeducators.com /dir/games/strategy_games/sprouts.asp (629 words)

	Salisbury Post \| LOCAL NEWS \| Game Game sprouts again (Site not responding. Last check: 2007-10-13)
		If you aren't familiar with our game, the Post is calling all gardeners to bring in, shall we say, "unique" produce.
		Margaret Fant of Salisbury won the Garden Game 26 years ago with her 27-inch stringless green beans.
		The oversized cabbage is the first entry of the Garden Game season.
	www.salisburypost.com /area/283862645061347.php (689 words)

	Directory - CDNet.com (Site not responding. Last check: 2007-10-13)
		Mathematical Games: Sprouts - Brief summary of the game.
		Sprouts: Analyzing a Simple Game - Mathematical analysis by the Illinois Mathematics and Science Academy.
		World Game of Sprouts Association - Association devoted to a serious exploration of the game.
	www.cdnet.com /cd/index.cgi?dir=/Games/Paper_and_Pencil/Sprouts (99 words)

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