Quelle est la différence entre un puzzle et une disposition des sièges?


Réponse 1:

Je fais l'hypothèse que par énigmes, vous entendez le jeu auquel les enfants jouent.

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!

 arrangements de pièces de puzzle.

Ainsi, la principale différence entre les puzzles et les sièges est que tous les arrangements ne sont pas valables pour un puzzle, alors que chaque siège peut être occupé par toute personne rendant tous les arrangements valides.

(Il est également possible de considérer

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.)