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#1 2011-12-24 00:52:20

juantheron
Member
Registered: 2011-10-19
Posts: 312

no. of points

find no. of points (x,y,z) in space whose each coordinate is a Negative Integer such that x+y+z+12 =0

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#2 2011-12-24 01:37:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: no. of points

let x'= |x| , y'= |y| and z'= |z|

then we have x'+y'+z'=12

so x'<12 and y'<12 and z'<12

since you are looking for the number of this points i think i can assume you mean points with integer coordinates.

since 0<x',y',z'<12

we have that x',y',z' are in the set {1,2,3,4,5,6,7,8,9,10,11} which has 11 elements.

so x',y' and z' have 11 possibilities each,and so do x,y and z.

the number of such points is: 11*11*11=11^3=1331 big_smile

Last edited by anonimnystefy (2011-12-24 02:17:59)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#3 2011-12-24 02:08:44

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: no. of points

Hi,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#4 2011-12-24 02:17:38

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: no. of points

hi gAr

oops! i think you're right.i forgot to take the condition x+y+z+12=0.i got the number of those which satisfy the equation x+y+z+12>0 smile


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2011-12-24 08:31:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: no. of points

Merry Christmas and Happy Holiday, gAr and
anonimnystefy.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2011-12-24 09:21:35

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: no. of points

it's not Christmas here yet.

we celebrate it on 7th of January.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2017-12-26 17:37:04

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 975

Re: no. of points

anonimnystefy wrote:

it's not Christmas here yet.

we celebrate it on 7th of January.

Wow, are you from Middle East?

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#8 2017-12-31 09:00:04

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,154
Website

Re: no. of points

Monox D. I-Fly wrote:

Wow, are you from Middle East?

I believe anonimnystefy is from Serbia. Orthodox Christians tend to celebrate Christmas on the 7th of January (as per the Julian calendar, which we don't use anymore -- we use the Gregorian calendar). Other countries do the same, like Russia.

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#9 2018-01-01 14:41:26

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 975

Re: no. of points

Isn't Serbia located in Middle East?

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#10 2018-01-01 14:47:53

ganesh
Administrator
Registered: 2005-06-28
Posts: 23,578

Re: no. of points

Hi Monox D. I-Fly,

Serbia, officially the Republic of Serbia, is a landlocked country situated at the crossroads of Central and Southeast Europe in the southern Pannonian Plain and the central Balkans. It borders Hungary to the north; Romania and Bulgaria to the east; Macedonia to the south; Croatia, Bosnia, Montenegro to the west and claims a border with Albania through the disputed territory of Kosovo. Serbia numbers around 7 million residents; its capital, Belgrade, ranks among the oldest and largest cities in Southeastern Europe.

Located in the continent of Europe, Serbia covers 77,474 square kilometers of land, making it the 118th largest nation in terms of land area.

Serbia became an independent state in 1878, after gaining its sovereignty from Turkey. The population of Serbia is 7,276,604 (2012) and the nation has a density of 94 people per square kilometer.

The currency of Serbia is the Serbian Dinar (RSD). As well, the people of Serbia are refered to as Serbian.

The dialing code for the country is 381 and the top level internet domain for Serbian sites is .rs.

Serbia shares land borders with 8 countries: Macedonia, Albania, Bulgaria, Romania, Croatia, Bosnia and Herzegovina, Hungary, Montenegro.

Source : https://www.worldatlas.com


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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