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Bot: Migrating 9 interwiki links, now provided by Wikidata on d:q1091301 (Report Errors)

← Older revision		Revision as of 15:42, 26 February 2013
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	~~Claude~~ is ~~her~~ name ~~and she~~ [~~http:~~//~~www~~.~~volvocars~~.~~com~~/us/~~sales-services~~/~~sales/volvo_certified_preowned/Pages/default~~.~~aspx totally digs~~] ~~that title~~. ~~Her buddies say~~ it's not ~~good for her but what she loves doing is flower arranging and she~~ is ~~attempting~~ ~~[http~~:~~//www~~.~~ebc-clan~~.~~ch/index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~12304 auto warranty] to make~~ [http://~~www~~.~~battdouglas~~.~~com~~/~~ActivityFeed/MyProfile/tabid/61/userId/6189/Default~~.~~aspx extended car warranty] auto warranty it a occupation~~. ~~Managing~~ ~~car [http://Www~~.~~nbcnews~~.~~com/id/23147777/ns/business~~-~~consumer_news/t/auto~~-~~warranty~~-~~firms~~-~~launch~~-~~sleazy-scam~~/ ~~warranty individuals~~] ~~is how I make money and it~~'~~s something I really enjoy~~. ~~Some time in the past I chose to reside in Arizona but I require to move for my family members~~.~~<br><br>Here is my web page~~ ... [http://~~glskating~~.~~com~~/~~groups~~/~~great-ideas-about-auto-repair-that-you-can-use/ glskating~~.~~com~~]		'''Mousetrap''' is the name of a game introduced by the [[English people\|English]] [[mathematician]] [[Arthur Cayley]]. In the game, cards numbered <math>1</math> through <math>n</math> ("say thirteen" in Cayley's original article) are shuffled to place them in some random [[permutation]] and are arranged in a circle with their faces up. Then, starting with the first card, the player begins counting <math>1, 2, 3, ...</math> and moving to the next card as the count is incremented. If at any point the player's current count matches the number on the card currently being pointed to, that card is removed from the circle and the player starts all over at <math>1</math> on the next card. If the player ever removes all of the cards from the permutation in this manner, then the player wins. If the player reaches the count <math>n+1</math> and cards still remain, then the game is lost.

			In order for at least one card to be removed, the initial permutation of the cards must not be a [[derangement]]. However, this is not a sufficient condition for winning, because it does not take into account subsequent removals. The number of ways the cards can be arranged such that the entire game is won, for ''n'' = 1, 2, ..., are
			: 1, 1, 2, 6, 15, 84, 330, 1812, 9978, 65503, ... {{OEIS\|A007709}}.

			==References==
			*{{citation
			\| last = Cayley \| first = Arthur \| author-link = Arthur Cayley
			\| journal = Quarterly Journal of Pure and Applied Mathematics
			\| pages = 8–10
			\| title = On the game of Mousetrap
			\| volume = 15
			\| year = 1878}}. [http://resolver.sub.uni-goettingen.de/purl?PPN600494829_0015 University of Göttingen Göttinger Digitalisierungszentrum (GDZ) scan]
			*{{citation
			\| last1 = Guy \| first1 = Richard K. \| author1-link = Richard K. Guy
			\| last2 = Nowakowski \| first2 = Richard J.
			\| editor1-last = Miklos \| editor1-first = D.
			\| editor2-last = Sos \| editor2-first = V. T. \| editor2-link = Vera T. Sós
			\| editor3-last = Szonyi \| editor3-first = T.
			\| contribution = Mousetrap
			\| mr = 1249712
			\| pages = 193–206
			\| series = Bolyai Society Math. Studies
			\| title = Combinatorics, Paul Erdős is Eighty
			\| volume = 1
			\| year = 1993}}.
			*{{citation
			\| last = Mundfrom \| first = Daniel J.
			\| doi = 10.1006/eujc.1994.1057
			\| issue = 6
			\| journal = [[European Journal of Combinatorics]]
			\| mr = 1302079
			\| pages = 555–560
			\| title = A problem in permutations: the game of 'Mousetrap'
			\| volume = 15
			\| year = 1994}}.
			*{{citation
			\| last = Spivey \| first = Michael Z.
			\| doi = 10.1016/j.ejc.2008.04.005
			\| issue = 2
			\| journal = [[European Journal of Combinatorics]]
			\| mr = 2489284
			\| pages = 532–539
			\| title = Staircase rook polynomials and Cayley's game of Mousetrap
			\| url = http://www.math.ups.edu/~mspivey/MousetrapFinal2.pdf
			\| volume = 30
			\| year = 2009}}.

			== External links ==
			* {{MathWorld\|urlname=Mousetrap\|title=Mousetrap}}

			[[Category:Mathematical games]]


			{{combin-stub}}

203.110.243.22 at 05:25, 30 July 2012

2012-07-30T05:25:57Z

New page

Claude is her name and she [http://www.volvocars.com/us/sales-services/sales/volvo_certified_preowned/Pages/default.aspx totally digs] that title. Her buddies say it's not good for her but what she loves doing is flower arranging and she is attempting [http://www.ebc-clan.ch/index.php?mod=users&action=view&id=12304 auto warranty] to make [http://www.battdouglas.com/ActivityFeed/MyProfile/tabid/61/userId/6189/Default.aspx extended car warranty] auto warranty it a occupation. Managing car [http://Www.nbcnews.com/id/23147777/ns/business-consumer_news/t/auto-warranty-firms-launch-sleazy-scam/ warranty individuals] is how I make money and it's something I really enjoy. Some time in the past I chose to reside in Arizona but I require to move for my family members.<br><br>Here is my web page ... [http://glskating.com/groups/great-ideas-about-auto-repair-that-you-can-use/ glskating.com]

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en>Addbot: Bot: Migrating 9 interwiki links, now provided by Wikidata on d:q1091301 (Report Errors)

203.110.243.22 at 05:25, 30 July 2012