JotD / QotD Ελληνική Λίστα Κουίζ (QotD)


Θέμα: Re: Manabhs



(nil): Basilios Solachidis (bsolachi(@)math.auth.gr)
Ημερομηνία: Mon 07 Dec 1998 - 11:00:55 EET

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
II II II II II II II II
IIIII IIII IIIIIII IIIIIII IIII

On Sun, 6 Dec 1998, Kaminogiannakis George wrote:

> 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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