From: sygelaki(@)ccf.auth.gr
Date: Πεμ 28 Νοε 2002 - 02:37:51 EET

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  Kalispera ki apo mena...Eipa na kanw tin arxi stin lista linontas auto to endiaferon provlima...

Tha xwrisoume tis lires se 3 meri me 4 lires i kathe mia tin A1={a1, a2, a3, a4} A2={b1, b2, b3, b4} A3= {c1, c2, c3, c4} alla austira etsi opws to dinw kai arithmimenes oi lires.
Stin prwti zigisi sigrinoume tis lires twn 2 prwtwn omadwn A1 kai A2.
1h zigisi :
a1 a2 a3 a4 me b1 b2 b3 b4

Tote :

(i) H zigaria isoropei. Tote i kalpiki lira tha
vriskete stin omada A3 kai oi lires stis 2 prwtes omades einai kanonikes tis opoies tis onomazoume K

2h zigisi : c1 c2 c3 me K K K
Tote an zigaria isoropisei kalpiki einai i c4

3h zigisi : c4 me K.
Vriskoume etsi an i kalpiki lira einai variteri i elafriteri. An i zigaria girei pros tin meria twn c1, c2, c3 tote i kalpiki einai metaksi twn c1, c2 ,c3 kai einai variteri. An kanoume akoma mia zigisi vriskoume poli eukola tin kalpiki zigizontas c1 kai c2. An isoropisei tote h kalpiki einai h c3. An girei se mia apo tis c1 h c2 tote einai i pio varia& An h zigaria girei pros ti meria twn K,K.K tote h kalpiki einai anamesa stis c1, c2, c3 kai einai elafriteri. Me mia akomi zigisi loipon vriskoume poli eukola tin kalpiki kai i diadikasia einai i idia opws kai prin me tis c1, c2 kai c3.

(ii) H zigaria gernei pros ti meria tis omadas A1

Tote i kalpiki einai eite stin omada A2 kai einai elafriteri eite stin A1 kai einai variteri

2h zigisi: a1 a2 b1 me b2 a3 a4

periptwseis :
(A) An i zigaria isoropisei tote kalpiki einai mia apo
tis b3 h b4 kai einai elafriteri

3h zigisi : b3 me b4
Tote plasti einai i elafriteri

(B) An h zigaria geirei pros tin meria twn a1, a2, b1
tote oi lires b1, a3, a4 einai kanonikes. H kalpiki einai eite mia apo tis a1, a2 kai einai variteri eite einai h b2 pou einai elafriteri

3h zigisi : a1 me a2
Tote an i zigaria isoropisei, kalpiki einai i b2 kai an den isoropisei tote kalpiki einai i variteri

(C) An i zigaria geirei pros tin meria twn b2, a3, a4
tote oi lires a1, a2, b2 einai kanonikes.H kalpiki einai mia apo tis a3, a4 kai einai variteri eite einai h b1 h opoia einai kai elafriteri.

3h zigisi : a3 me a4
An I zigaria isoropisei tote i kalpiki einai h b1 kai an i zigaria den isoropisei tote kalpiki einai i variteri

(iii) H zigaria gernei pros tin meria tis omadas A2
Tote i apodeiksi einai idia opws kai stin periptwsi
(ii)

Auti einai i lisi pou exw na dwsw egw gia to poli oraio auto provlima me tin opoia vgazoume kai to simperasma gia to an i kalpiki auti lira sto provlima einai variteri eite elafriteri kai den menoume mono stin gnisiotita tis&
Alexandros or CretanMan

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