From: Basilios Solachidis (bsolachi(@)math.auth.gr)
Date: Δευ 07 Δεκ 1998 - 11:00:55 EET

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Basika exw tin entypwsi pws to apotelesma tou filou den einai swsto.(ENTYPWSH)

kanontas mia analusi exoume:
Estw ta 4 swsta bari a,b,c,d
Ta dynata "athroismata" tous einai k1*a+k2*b+k3*c+k4*d opou k1,k2,k3,k4=0,-1,+1 (0 an den xrisimopoiisoume to baros 1, an to baloume apo to allo zygi
-1 an to baloume apo to idio zygi me to baros pou theloume na zyisoume)

etsi exoume 3^4=81 dynata athroismata
1 athroisma apo ta 81 einai to 0 (k1=k2=k3=k4=0 to opoio aporriptetai) Gia ta ypoloipa athroismata exoume: ta misa (40) einai thetika kai ta alla misa arnitika (ta arnitika tous (an bazw opou 1 to -1 kai opou -1 to 1)) Synepws me ta 4 auta bari mporoume na paroume 40 diaforetika athroismata. Emeis theloume na zygisoume 40 bari (apo to 1 ws to 40)ara 1)exoume synolika 40 athrismata kai gia na sumperilaboume ola ta bari prepei ->kathe syndiasmos barwn na dinei diforetiko baros (giati an ena baros mporei na bgei me dyo px syndyasmous tote tha den tha mporoume na exoume syndiasmous gia ta upoloipa bari ) diladi oi syndiasmoi bgazoun apo 1 ws 40 (apo mia fora) 2)Den bgazoun panw apo 40 , ara to athroisma tous einai akribws 40.

Ara
psaxnw gia 4 arithmous pou to athroisma tous einai 40 kai den ginetai na bgazoun ena "athroisma" me dyo tropous (px den mporoun na exoun to 1 kai to 2 giati to athroisma 1 bgainei me to 1 kai me 2-1)

Mia lusi einai (den kserw an einai i monadiki) 1-3-9-27 (dynameis tou 3)

Epekteinontas to problima mporoume na exoume 5 bari pou na metroun apo 1 ws 121 (lisi 1-3-9-27-81) i genikotera N bari pou na metroun apo 1 ws (3^N-1)/2 (me lusi 1-3-9-27-...-3^(N-1))

IIIII IIII IIII IIII III III

II  II  II   II      II      II  II
II  II  II   II      II       IIII
IIIII   II   II      II        II
II  II  II   II      II        II

> ta varakia pou exei einai 30-5-3-2
> an thelei na zigisei kapio allo varos p.x.
> an thelei na valei 1 kilo zaxari, tote vazei to varaki twn 2 kgr apo th
> mia kai afto twn 3 kgr apo thn allh kai simplirwnei th zaxari mexri na
> isoropisei i zigaria
> an kapios thelei gia paradeigma 11 kil tha xreiastei na kanei 2 zigiseis
> sth mia tha valei ta 10 kila kai sthn allh zigisi to 1
> an einai o pelatis periergos kai thelei 16 kila, (tha faei tetio
> vlastimidi pou tha to metaniwsei amesws afenos) kai afeterou th kanei 3
> zigiseis.
> mia gia ta 10 kila (xrisimopoiwntas ta varakia 5-3-2)
> meta ta 5 kila (xrisimopoiontas to 5kilo varaki) kai telos to ena kilo me
> th diadikasia pou periegrapsa parapanw
> etsi mporei na zigisei opoio varos thelei o pelatis (pou exei panta dikio)
> moirazontas to se mikrotera vari
>
>
>
>
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