Was ist der Unterschied zwischen einem Puzzle und einer Sitzanordnung?


Antwort 1:

Ich gehe davon aus, dass Sie mit Rätseln das Spiel meinen, das Kinder spielen.

Ifyouconsidernseatsand[math]n[/math]peoplethenyouwillhave[math]n![/math]possibleseatingarrangements.Inthiscaseanyoneisabletooccupyanyseat(aslongasithasntbeentakenalready).If you consider n seats and [math]n[/math] people then you will have [math]n![/math] possible seating arrangements. In this case anyone is able to occupy any seat (as long as it hasn't been taken already).

Nowifyoutakealookatpuzzles,itreallydependsontheshapeofthepieces.Usually,notallpiecesarethesame.Forexample,thepiecesontheedgecantgointhecenter.Soeverypiececantoccupyanypositionandthus,therewillbelessthann!puzzlepiecearrangements.Now if you take a look at puzzles, it really depends on the shape of the pieces. Usually, not all pieces are the same. For example, the pieces on the edge can't go in the center. So every piece can't occupy any position and thus, there will be less than n! puzzle piece arrangements.

seatsandnpeoplethenyouwillhave[math]n![/math]possibleseatingarrangements.Inthiscaseanyoneisabletooccupyanyseat(aslongasithasntbeentakenalready). seats and n people then you will have [math]n![/math] possible seating arrangements. In this case anyone is able to occupy any seat (as long as it hasn't been taken already).

(Itisalsopossibletoconsidermpeoplefor[math]n[/math]seatswhere[math]mn[/math].Inthiscase,therewillbe[math]n!(nm)![/math]arrangementsbecausewehavetodivideoutbythenumberofwaysthe[math]nm[/math]emptyseatscouldbearranged.)(It is also possible to consider m people for [math]n[/math] seats where [math]m\le n[/math]. In this case, there will be [math]\frac{n!}{(n-m)!}[/math] arrangements because we have to divide out by the number of ways the [math]n-m[/math] empty seats could be arranged.)

n!n!

 Puzzleteileanordnungen.

Der Hauptunterschied zwischen Rätseln und Sitzarrangements besteht darin, dass nicht alle Arrangements für ein Rätsel gültig sind, wohingegen jeder Sitzplatz von jeder Person belegt werden kann, die alle Arrangements gültig macht.

(Es ist auch möglich, in Betracht zu ziehen

mm

peoplefornseatswhere[math]mn[/math].Inthiscase,therewillbe[math]n!(nm)![/math]arrangementsbecausewehavetodivideoutbythenumberofwaysthe[math]nm[/math]emptyseatscouldbearranged.) people for n seats where [math]m\le n[/math]. In this case, there will be [math]\frac{n!}{(n-m)!}[/math] arrangements because we have to divide out by the number of ways the [math]n-m[/math] empty seats could be arranged.)