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Задача разновесов или гирь
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shgalex
Posted: Feb 7 2007, 20:43

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Даны 13 гирь(или разновесов).Известно ,что вес каждой --натуральное число.Из них ,то есть 13-ти гирь(или разновесов), любые 12 МОЖНО разбить на два равных (по шесть) подмножества в которых сумарный вес так же равен.
Н А Д О Д О К А З А Т Ь Ч Т О все эти гири-разновесы имеют равный вес.

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gevpa
Posted: Feb 10 2007, 17:13

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Unenq hetevjaly:
(A) a1, a2, ..., a13
Gientq vor nrancic kamayakan 12 - y kareli e bajanel 2 xmbi aynpes vor gumarnery linen irar havasar.

Ditarkenq hetevjal bazmutyuny:
(B) b1 = a1 - k, b2 = a2 - k, ... , b13 = a13 - k ( k <= min(a1, a2, ... a13 ) )

Ete (A) bazmutyan kamayakan 12 elementanoc bazmutyun hnaravaor e trohel 2 havasaragumar bazmutyunneri,
apa (B) - i nuyn hamarneric baxkacac entabazmutyuny nmanapes. Ev hakaraky (B) - ic hetevum e (A) - i trohumy.

Ditarkenq xndiry k = min(a1, a2, ..., a13) depqum.
Yndhanrutyuny chxaxtelov entadrenq a13 = min(a1, a2, ..., a13).
Kstananq hetevyal bazmutyuny : b1 = a1 - a13, ..., b12 = a12 - 13, b13 = 0
Gitenq vor`
b1 + b2 + ... + b11 + b12 = 2 * k1
b1 + b2 + ... + b11 + b13 = 2 * k2
b12 - b13 = 2 * (k1 - k2) => b12 = 2 * (k1 - k2)

Hetevabar karogh enq pndel hetevyaly`
B bazmutyan kamayakan element zuyg e:
Ynd vorum elementneric meky(b13) - y havasar e 0:

Ditarkenq hetevyal bazmutyuny`
( C ) c1 = b1 / 2, c2 = b2 / 2, ... , c13 = b13 / 2

Hesht e tesnel vor ( C ) - xndiry hamarjeq e (B) - in.

Sharunak bajanelov bolor elementnery erkusi kstananq xndirner voronq hamarjeq en skzbnakanin,
aysinqn kamayakan 12 - y hnaravor e trohel havasarazor bazmutyunneri, voric inchpes menq enq cuyc
tvel hetevum e vor nranq bolory zuyg en(hetevum e nrancic meki 0 linelu depqum).
Aysinqn amen bajanumic heto arajacac elementnery petq e linen zuyg.
Bayc bajanumneri ardyunqum kstananq element havasar 1 - in, vory zuyg che, aysinqn
(B) bazmutyan bolor elementnery petq e linen 0 (xndri paymani depqum), voric el hetevum e
vor (A) bazmutyan bolor elementnery havasarn en b13 - in, aysinqn havasar en irar.


 
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Dream_InspectoR
Posted: Feb 10 2007, 19:08

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Ernek havesid Paruyr smile.gif) Ed b-eri gumar@ vorteghic gitenq vor vir 2k1 ev 2k2 a?

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Kill'em!!! Kill'em ALL!!!
 
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gevpa
Posted: Feb 11 2007, 23:26

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QUOTE (In the immortal words of Dream_InspectoR, since Feb 10 2007, 19:08...)
Ernek havesid Paruyr smile.gif) Ed b-eri gumar@ vorteghic gitenq vor vir 2k1 ev 2k2 a?

Haves et pahin unei Styop jan smile.gif
Inch verabervum a inchi a b - eri gumary 2 * k:
Galis a en pastic vor 12 b - er kareli a trohel erku xmbi voronq havasaragumar en, asenq yuraqanchyury havasar e k -i,
hetevabar 12 - i gumary klini 2 * k.
 
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shgalex
Posted: Feb 13 2007, 14:22

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Shat shat mersi Paruyr jan. Qo lucumy indz mek urish lucum tvec.
Menak verchabant lav chhaskaca. Ete djvar chi mihat aveli parz bacatri
datogutyunnert.
QUOTE
...Aysinqn amen bajanumic heto arajacac elementnery petq e linen zuyg.
Bayc bajanumneri ardyunqum kstananq element havasar 1 - in, vory zuyg che, aysinqn (cool.gif bazmutyan bolor elementnery petq e linen 0 (xndri paymani depqum), voric el hetevum e vor (A) bazmutyan bolor elementnery havasarn en b13 - in, aysinqn havasar en irar.
??????????????????????
Im lucumy sae:
1.Cuic tanq vor bolor kshraqareri qashy kam kent tiv e kam zuiq.
13-ic yntrenq cankacac 12-y. 13-erordy kam kent e kam zuiq. Arden
yntrac 12-ic vercnenq mer veciaky. Ete 13-erord kshraqareri qashy
kent e(zuig e) apa mer veciakic kntrem mihat zuig(kent) ev tegerov kpoxem <yst xndri paimani 13 kshraqareric yntrvum e cankacac 12-y>. Anshusht gumary kxaxtvi. Hetevabar bolor kshraqareri qashy kam kent tiv e kam zuiq.
2. Nkatenq vor ete kshraqarery kent en apa boloric 1 hanelov xndri imasty chi poxvi. Hetevebar kenti depqy bervum e zuigi depqin.
3.Bajanenq bolor kshraqarery 2-i. Stacvac tveri hamar tanenq 1. ev 2.
datogutunery. Sharunakelov aispes kstananq
1 1 1 1 1 1 1 1 1 1 1 1 1 -- 13 hat 1.
ev verg. tongue.gif

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gevpa
Posted: Feb 13 2007, 18:50

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QUOTE
... Qo  lucumy  indz  mek  urish  lucum  tvec.

Nor lucum smile.gif ? Uxxaki ogtagorcel es bolor druytnery dzevakerpvac bervac apacuyci mej smile.gif. Amen depqum.
Inch verabervum e harcid.
Cuyc er trvac vor ete elementneric meky 0 e apa bolor elementnery zuyg en.
2 - i bajaneluc 0 - akan elementy mnum e, hetevabar qani vor cuyc er tvac 2 - i bajaneluc stacvac u skzbnakan xndirneri hamarjequtyuny
hajord qaylum el bolory klinen zuyg. Bajanumneri ardyunqum anpayman khasnenq mi qayli erb kstananq 1 ( amenashaty log2( max( B ) ) qaylic )
hetevabar amenaskzbum kam bolor elementnery petq e linen 0 kam kganq hakasutyan.
 
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shgalex
Posted: Feb 13 2007, 19:57

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QUOTE (In the immortal words of gevpa, since Feb 13 2007, 18:50)
Nor lucum smile.gif ?

Es Nor bary chem ogtagorcel ,isk qo bolor druytnery ev im druytnery mej tarberutun ka.
evs mek angam mersi.

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gevpa
Posted: Feb 14 2007, 12:10

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Mek urish lucum == nor lucum smile.gif

Xndrem.
 
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