JotD / QotD Ελληνική Λίστα Κουίζ (QotD)


Θέμα: Re: Xrwmatistes mpilies (APANTHSH)



(nil): Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Ημερομηνία: Δευ 30 Ιούν 2003 - 14:46:12 EEST

Kalhmera. Exoume kai leme...

Estw x o arxikos ari0mos xrwmatwn, kai n mpilies apo to ka0e xrwma.
Profanws loipon exoume arxika nx mpilies. H pi0anothta na einai idiou
xrwmatos duo tuxaia epilegmenes mpilies isoutai me :

p = (n - 1) / (nx - 1)

(Prokeitai sthn ousia gia thn pi0anothta na einai h DEUTERH mpilia sto
xrwma ths PRWTHS, to phliko eunoikwn pros dunata endexomena).

Ustera apo tis 20 pou pros0esame, h pi0anothta einai to a0roisma duo orwn :

p = nx/(nx+20) * (n-1)/(nx+19) + 20/(nx+20) * 19/(nx+19)

O prwtos oros ekfrazei thn pi0anothta na epile3oume ws prwth mpilia mia
apo tis palies (nx/(nx+20)) kai, dedomenou autou, na epile3oume ws deuterh
mia tou idiou xrwmatos ((n-1)/(nx+19)). Paromoiws kai gia to deutero oro,
alla gia tis kainouries 20 mpilies.

Oi duo autes pi0anothtes einai ises, mas leei to provlhma. Ustera apo ligh
stoixeiwdh algevra katalhgoume sthn e3iswsh :

19 = (21-2n) x

Ara to x diairei to 19 kai isoutai h me 1 h me 19.

Den mporei na isoutai me 1, giati tote n=x=1 kai oi pi0anothtes xanoun to
nohma tous.

Ara x=19, opote n=10. Dhladh, sthn arxh eixame 19 xrwmata, me 10 mpilies
apo to ka0ena.

Parempiptontws, vazontas autes tis times sthn arxikh parastash exoume
pi0anothta 1/21 gia duo mpilies idiou xrwmatos.

Epituxontes :

Vaggelis Kapoulas
Theofanis Gkountras
George Papargiris
Manolis Fanourgakis

(Pi0anon na 3exasa kapoion, an nai peite mou).

Kala na pernate,

Dimitris

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