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Rundtisch-Permutationen and Ringsymmetrien

 

p.specht

for Reihen-erections counts The known Permutationsformel x = n ! (speak "n Faktorielle"), namely x = n * (n-1) * (n-2) * ... To 1 down. with 1 To multiplizieren Change but naturally nothing more on the Result, means is the eigentliche Runterzählgrenze The 2.

with Sitzordnungen on Rundtischen distinguish one but end and beginning not. there's therefore circa a filled turn (=n burst) less unterschiedlichen Anordnungsmöglichkeiten, therefore sounds The Formel x = (n-1)*(n-2)*... *2 or.
"Faktorielle of (n-1)".

with Armreifen with on the ripe gleichverteilten Schmucksteinen is as Another factor To respect, that the ring indeed umgedreht on the table laid go can. Rückläufige orders the stones go therefore of rechtläufigen not distinguished, The Formel sounds therefore x = (n-1)*(n-2)*... * 3 or. x = 1/2 * Faktorielle of (n-1). the nachstehene Progi shows, wieviele Unikate such Schmuckreifen manufactured go can, and resolve so one altes maths-puzzel.
Window Title upper$("   R I n G s Y M M E T R I E :    "+\
"A r m r e i f s c h m u c k s t e i n m u s t e r p r o b l e m")
AppendMenubar 100, "By homepages.fh-friedberg.de/boergens/trouble/problem_01_09loe.htm"
Declare i&
Cls
print "\n an firm sales golden Armreifen with verschiedenfarbigen"
print " Schmucksteinen gleichverteilt on the amplitude. Wievielen Käufern kann"
print " with n unterschiedlichen Schmucksteinen guaranteeing one Unikat   "
print " involved the pattern, the The stones form, sales go ?"
print " [Button]":waitinput :cls:print:font 2
print " Number of Schmucksteine   amount möglicher Unikate ":print

whileloop 29:i&=&Loop

    print mkstr$(" ",20-len(st$(i&)))+st$(i&);tab(32);
    print translate $(stature$("%g",round(faku(i&-1)/2,0)),"E0"," * 10 ^ ")

endwhile

waitinput:Print " Ciao!"
waitinput 4000:End

proc faku :parameters i&:var prod!=1

    whileloop i&:prod!=prod!*&Loop:endwhile:return prod!

    endproc

 
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05/20/21  
 



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Hans Neff01/24/23
p.specht11/21/21
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