JotD / QotD Ελληνική Λίστα Κουίζ (QotD)


Θέμα: Re: Me to eurw kalutera (APANTHSH)



(nil): Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Ημερομηνία: Tue 03 Jun 2003 - 11:16:50 EEST

Kalhmera. Sas kakoma0a me auto to provlhma giati mou apanthse lao0alassa.
An kai, ap' o,ti katalavainw, anastena3an ta CPUs. Ts, ts, ts...:-)

Estw oti h epitagh htan gia x eurw kai y lepta. Tote h pelatissa eprepe na
eixe parei 100x + y lepta.

Ant' autou, 3eroume oti phre 100y + x lepta. (Profanws o tamias oute pou
koita3e to noumero olografws.)

3odeye 50 apo auta, kai ths emeinan 100y + x - 50, ta opoia einai
triplasia tou posou ths epitaghs.

Dhladh 100y + x - 50 = 3 (100x + y) <=> 97y - 299x = 50, me ton periorismo
oti x,y akeraioi meta3u tou 0 kai tou 99 sumperilamvanomenwn. Auth h
diofantikh e3iswsh mporei na fainetai daimonas, alla aplopoieitai kanontas
kapoies diaireseis (299:97 = 3 upoloipo 8, 97:8 = 12 upoloipo 1)

Lamvanontas etsi upoyh oti 97 = 8 . 12 + 1 ka0ws kai 299 = 8 . 37 + 3 h
e3iswsh mas metatrepetai se 8(12y - 37x) + y - 3x = 50, mia e3iswsh ths morfhs
8a + b = 50 me a,b akeraious.

Mia lush einai a = 6, b = 2. Mporoume na paroume apeires luseis
pros0etontas/afairwntas 1 sto/apo to a gia ka0e 8 pou afairoume/pros0etoume
apo to/sto b.

Wstoso, an to b einai megalutero tou 2, auto mas dinei perissotera twn 100
eurw. Omoiws, an to b einai mikrotero tou 2, auto mas dinei arnhtiko ari0mo
eurw. O elegxos autos einai eukolos afou ta eurw x = 12b - a.

Ara, a = 6 kai b = 2. Auto mas dinei x = 18 kai y = 56, dhladh h epitagh
htan gia 18 eurw kai 56 lepta.

(Kai h pelatissa phre 56 eurw kai 18 lepta. Siga mhn evgaze kouventa !)

Epituxontes :

Kwnstantinos Tampouris
Vaggelis Kapoulas
Theodore Triantafullopoulos
Theofanis Gkountras
George Papargiris
Irene Papaeconomou
Giwths Kokkalhs
nav17
Manolis Fanourgakis
Nikos Karantzoulis
Dionisios Belekoukias
Giorgos Makris
Nikos_K
Yiannis Papagrigorakis
Alexandros Droseltis

Kala na pernate,

Dimitris

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