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> Majmun Koji Prica, I nema veze sa zadatkom

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pyost
post Dec 28 2007, 05:03 PM
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Evo ga jedan zadatak koji me zestoko je*e u mozak XD.gif

Slupa se brod i prezivi 5 mornara koji se dovuku do pustog ostrva. Tu naidju na majmuna koji im kaze da su na ostrvu jedino jestivi kokosovi orasi. Mornari nakon toga odluce da skupljaju kokosove orahe, i na kraju ih skupe n, n > 10000, i odu na spavanje.

Tokom noci se jedan mornar probudi i odluci da uzme svoj deo. On je tih n oraha podelio na 5 jednakih delova, jedan deo zadrza, pri cemu mu je ostao orah viska, koga je dao majmunu, pa se vratio da spava. Onda je naisao drugi mornar i ponovio isti postupak - podelio gomilu na pet delova, jedan deo zadrzao, a jedan orah dao majmunu. Isto su uradila i ostala 3 mornara.

Kada je svanulo, primetili su da se gomila smanjila, ali su cutali, posto je svako uzeo svoj deo. Tu malu gomilu sto je ostala ponovo su podelili na 5 delova, a orah viska (koje iznenadjenje) su dali majmunu.

Koliko je bilo oraha na pocetku?

S obzirom da nam nije dato koliko je oraha na kraju svaki mornar imao, pretpostavljam da se trazi resenje u opstem obliku unsure.gif


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username
post Dec 28 2007, 05:07 PM
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kad si pomenuo majmuna koji prica:
"Na Univerzitetu tom i tom je prodrmana teorija da je covek pametniji od majmuna." biggrin.gif lol.gif
sa vesti B92
edit: ovo `ostao mu je jedan viska` je li to ostatak pri deljenju oraha na 5 delova?

kako se pise znak za kongruenciju?

This post has been edited by username: Dec 28 2007, 05:09 PM
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pyost
post Dec 28 2007, 05:18 PM
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U LaTeXu?

CODE
n \equiv 2 \, ( mod \, 3)


n \equiv 2 \, ( mod \, 3)


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Nostradamus
post Dec 28 2007, 05:18 PM
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QUOTE(pyost @ Dec 28 2007, 05:03 PM)
Evo ga jedan zadatak koji me zestoko je*e u mozak XD.gif

Slupa se brod i prezivi 5 mornara koji se dovuku do pustog ostrva. Tu naidju na majmuna koji im kaze da su na ostrvu jedino jestivi kokosovi orasi. Mornari nakon toga odluce da skupljaju kokosove orahe, i na kraju ih skupe n, n > 10000, i odu na spavanje.

Tokom noci se jedan mornar probudi i odluci da uzme svoj deo. On je tih n oraha podelio na 5 jednakih delova, jedan deo zadrza, pri cemu mu je ostao orah viska, koga je dao majmunu, pa se vratio da spava. Onda je naisao drugi mornar i ponovio isti postupak - podelio gomilu na pet delova, jedan deo zadrzao, a jedan orah dao majmunu. Isto su uradila i ostala 3 mornara.

Kada je svanulo, primetili su da se gomila smanjila, ali su cutali, posto je svako uzeo svoj deo. Tu malu gomilu sto je ostala ponovo su podelili na 5 delova, a orah viska (koje iznenadjenje) su dali majmunu.

Koliko je bilo oraha na pocetku?

S obzirom da nam nije dato koliko je oraha na kraju svaki mornar imao, pretpostavljam da se trazi resenje u opstem obliku unsure.gif
*



Pa mozda se grdno varam, ali zar ne kaze da je oraha bilo n


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(a,b) \sim (c,d) \Leftrightarrow (a - c) \in \mathbb{Z} \wedge (b - d) \in \mathbb{Z}

\mathbb{T}^2\equiv\mathbb{R}^2/\sim
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pyost
post Dec 28 2007, 05:19 PM
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Ma... XD.gif Treba naci N u obliku tipa "4x + 6, x > 13".


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username
post Dec 28 2007, 05:23 PM
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n \equiv 1 \, ( mod \, 5)

(n-1)/ 5 \equiv 1 \, ( mod \, 5)

(((n-1)/ 5)-1)/5 \equiv 1 \, ( mod \, 5)

[[(((n-1)/ 5)-1)/5]-1]/5 \equiv 1 \, ( mod \, 5)

{{[[(((n-1)/ 5)-1)/5]-1]/5}-1}/5 \equiv 1 \, ( mod \, 5)

{{{[[(((n-1)/ 5)-1)/5]-1]/5}-1}/5}-1 \, pa \, sve \, sa \, 5 \equiv 1 \, ( mod \, 5)

e ne znam da ga zapisem
nego, nesto sam kliknuo na tastaturi i sad mi je uvecano ovo sto vidim na ekranu

This post has been edited by pyost: Dec 28 2007, 05:31 PM
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pyost
post Dec 28 2007, 05:25 PM
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Intelegencija... LaTeX kod ide izmedju FOR tagova.


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username
post Dec 28 2007, 05:27 PM
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e pa hebi ga mad.gif
sad je bolje biggrin.gif

This post has been edited by username: Dec 28 2007, 05:29 PM
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pyost
post Dec 28 2007, 05:32 PM
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Bas ti i nije neko resenje XD.gif


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username
post Dec 28 2007, 05:34 PM
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nije kraj
dakle sad:
ili naci takve brojeve ili dokazati indukcijom da ne postoje
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pyost
post Dec 28 2007, 05:35 PM
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Ja i dalje stojim pri tome da nije neko resenje biggrin.gif


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username
post Dec 28 2007, 05:37 PM
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dobro, dobro
1) uzmemo 10001
10001-1=10000
10000/5=20000
sto nije kongruentno sa 1 po modulu 5
2)pretpostavimo da je gore navedeno nemoguce
3)dokazimo da tada ne vazi za n+1
i to je to laugh.gif
gotov zadatak biggrin.gif
a odgovor: to je nemoguce lol.gif

This post has been edited by username: Dec 28 2007, 05:37 PM
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Hannibal Lecter
post Dec 28 2007, 05:40 PM
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Dakle
ako je kad su se probudili bilo t oraha onda je
-pre 5. budjenja bilo 5t+1
-pre 4. budjenja bilo 5*(5t+1)+1=25t+6
-pre 3. budjenja bilo 5*(25t+6)+1=125t+31
-pre 2. budjenja bilo 5*(125t+31)+1=625t+156
-pre 1. budjenja bilo 5*(625t+156)+1=3125t+1561

e a kako je t=5k+1 onda je n=3125*(5k+1)+1561=15625t+4686 biggrin.gif

Resenje: n=15625k+4686, k je prirodan broj lol.gif

This post has been edited by Noddy: Dec 28 2007, 05:49 PM


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And as we wind on down the road
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How everything still turns to gold
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When all are one and one is all
To be a rock and not to roll

Svi me žele, a ja sam nedodirljiv!
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username
post Dec 28 2007, 05:42 PM
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da ja sam isao kako je vreme teklo, a ti unazad smile.gif
to je to lol.gif
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Hannibal Lecter
post Dec 28 2007, 05:45 PM
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Mora da je negde greska u racunu jer kad se oduzme 1 ne dobija se broj == 0 (mod 5) sad.gif

edit: nasao sam gresku u mnozenju
sada bi trebalo da vazi...

This post has been edited by Noddy: Dec 28 2007, 05:49 PM


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And as we wind on down the road
Our shadows taller than our soul
There walks a lady we all know
Who shines white light and wants to show
How everything still turns to gold
And if you listen very hard
The truth will come to you at last
When all are one and one is all
To be a rock and not to roll

Svi me žele, a ja sam nedodirljiv!
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pyost
post Dec 28 2007, 05:51 PM
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QUOTE(Noddy @ Dec 28 2007, 05:40 PM)
-pre 5. budjenja bilo 5t+1
-pre 4. budjenja bilo 5*(5t+1)+1=25t+6
*



Ne moze.

Ako je x = 5t +1, to je 4/5 od onoga sto je pre 4. budjenja bilo, a ne 1/5. Odnosno:

-pre 5. budjenja bilo 5t+1
-pre 4. budjenja bilo 5*(5t+1)/4+1


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Hannibal Lecter
post Dec 28 2007, 05:55 PM
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right smile.gif


--------------------
And as we wind on down the road
Our shadows taller than our soul
There walks a lady we all know
Who shines white light and wants to show
How everything still turns to gold
And if you listen very hard
The truth will come to you at last
When all are one and one is all
To be a rock and not to roll

Svi me žele, a ja sam nedodirljiv!
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pyost
post Dec 28 2007, 05:56 PM
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A to prilicno komplikuje formulu...


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Hannibal Lecter
post Dec 28 2007, 05:58 PM
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Epa ja ne vidim drugacije resenje biggrin.gif
I mrzi me da razmisljam posto sam na raspustu wink.gif
Tako da iskljucujem se iz resavanja zadatka bye.gif bye.gif bye.gif


--------------------
And as we wind on down the road
Our shadows taller than our soul
There walks a lady we all know
Who shines white light and wants to show
How everything still turns to gold
And if you listen very hard
The truth will come to you at last
When all are one and one is all
To be a rock and not to roll

Svi me žele, a ja sam nedodirljiv!
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