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24 Jun 2004, 03:24
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#1
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Stoke
Join Date: Apr 2000
Posts: 92
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Maths people, enlighten me
There is a rule which states that a number diviedes by three if it's digits added together will also devide by three
for example, take the number 4572 is it divisable by 3?
4+5+7+2 = 18, so yes, the number is divisable by 3.
and according to the calculator 4572 devided by 3 is 1524
So, here's my question - how do you go about proving this rule mathematically?
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24 Jun 2004, 03:24
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#2
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Bored
Join Date: Apr 2001
Location: Nottm ->Shef ->Croydon ->Manc ->Durham ->Sheffield
Posts: 6,506
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Re: Maths people, enlighten me
it works - end of story.
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24 Jun 2004, 03:40
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#3
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Vermin Supreme
Join Date: Jul 2000
Location: Pittsburgh
Posts: 3,280
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Re: Maths people, enlighten me
abcde = a * 10000 + b * 1000 + c* 100 + d*10 + e
= a + 9999a + b + 999b + c + 99c + d + 9d + e
= (a + b + c + d + e) + (9999a + 999b + 99c + 9d)
the part on the right is obviously divisible by three, if the part on the left is divisible by three as well, the whole thing is
QED
(you woudl be more impressed if oyu knew how druknk i was)
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24 Jun 2004, 03:43
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#4
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Stoke
Join Date: Apr 2000
Posts: 92
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Re: Maths people, enlighten me
nice
did you generally know that or have to put thought into it?
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24 Jun 2004, 03:48
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#5
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Vermin Supreme
Join Date: Jul 2000
Location: Pittsburgh
Posts: 3,280
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Re: Maths people, enlighten me
Quote:
Originally Posted by '|'empest
nice
did you generally know that or have to put thought into it?
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thought about it.
wrote the first two lines in about a minute, stared at it while sipping beer for about five minutes, then added the third line with the exaplnantion.
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24 Jun 2004, 08:18
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#6
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Choice of Whacker sir?
Join Date: May 2001
Location: Ireland
Posts: 679
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Re: Maths people, enlighten me
Quote:
Originally Posted by acropolis
abcde = a * 10000 + b * 1000 + c* 100 + d*10 + e
= a + 9999a + b + 999b + c + 99c + d + 9d + e
= (a + b + c + d + e) + (9999a + 999b + 99c + 9d)
the part on the right is obviously divisible by three, if the part on the left is divisible by three as well, the whole thing is
QED
(you woudl be more impressed if oyu knew how druknk i was)
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man that formula is flawed as in it doesn't prove what waws oringially asked.
because the abcde can represent any number but not all numbers are divisable by 3
If number has four digits and each digit is represented by a(x),a(x+1),a(x+2,a(x+2)4...
if a(x) + a(x+1)/3 = even number
then the whole number is divisable by 3
oki bored will come back and fix
__________________
* thanos sets mode: -brain The_Shadow_Man
Last edited by TheShadowMan; 24 Jun 2004 at 08:24.
Reason: Gonna keep editing til i get proof
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24 Jun 2004, 08:21
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#7
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The Twilight of the Gods
Join Date: Jan 2001
Posts: 23,481
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Re: Maths people, enlighten me
Quote:
Originally Posted by TheShadowMan
man that formula is flawed as in it doesn't prove what waws oringially asked.
because the abcde can represent any number but not all numbers are divisable by 3
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No it can't you buffoon.
The question is: 'If a+b+c+d+e is divisable by 3, then why is abcde divisible by 3?'
It's been proven that abcde is divisible by 3 if a+b+c+d+e, because its a given in the question
It's like proving that d e^x /dx = e^x, then you coming along and saying 'Ah, but d x^2/dx =! e^x'.
THAT'S NOT THE QUESTION
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24 Jun 2004, 08:27
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#8
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Choice of Whacker sir?
Join Date: May 2001
Location: Ireland
Posts: 679
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Re: Maths people, enlighten me
yeh but you have prove that sum of digits are divisable by three to prove by the number is divisable by 3
else you can just say that the reason the number can be divided by 3 is because it is a multilpe 3
__________________
* thanos sets mode: -brain The_Shadow_Man
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24 Jun 2004, 08:35
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#9
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The Twilight of the Gods
Join Date: Jan 2001
Posts: 23,481
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Re: Maths people, enlighten me
Quote:
Originally Posted by TheShadowMan
yeh but you have prove that sum of digits are divisable by three to prove by the number is divisable by 3
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Ok, let me put this in a simpler way.
IT'S NOT DIVISIBLE BY THREE IF THE SUM OF THE DIGITS AREN'T DIVISIBLE BY THREE, SO PROVING INDEPENDENT OF WHAT 'A+B+C+D+E' IS IS NOT ONLY POINTLESS, IT'S ALSO IMPOSSIBLE
Quote:
Originally Posted by TheShadowMan
else you can just say that the reason the number can be divided by 3 is because it is a multilpe 3
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If it isn't a multiple of 3, it can't be divided integrally by 3. That's an obvious given to this little exercise dude.
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24 Jun 2004, 08:38
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#10
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Choice of Whacker sir?
Join Date: May 2001
Location: Ireland
Posts: 679
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Re: Maths people, enlighten me
ah so all numbers that divisable by three, those digits of those numbers all when added together are divisable by three.
I understand now it just wasn't clear in the question
__________________
* thanos sets mode: -brain The_Shadow_Man
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24 Jun 2004, 08:43
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#11
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The Twilight of the Gods
Join Date: Jan 2001
Posts: 23,481
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Re: Maths people, enlighten me
Quote:
Originally Posted by TheShadowMan
I understand now it just wasn't clear in the question
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Why not read the first line of the thread?
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24 Jun 2004, 08:50
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#12
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Registered User
Join Date: Feb 2002
Location: South Pacific
Posts: 4,911
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Re: Maths people, enlighten me
every third integer starting at 3, divided by 3 is an integer.
__________________
I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Jun 2004, 10:58
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#13
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Registered User
Join Date: Jun 2000
Posts: 8,476
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Re: Maths people, enlighten me
10.002
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24 Jun 2004, 11:24
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#14
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Registered User
Join Date: Feb 2002
Location: South Pacific
Posts: 4,911
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Re: Maths people, enlighten me
Quote:
Originally Posted by Nodrog
10.002
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true dat.
__________________
I think it's time we blow this scene, get everybody and the stuff together..........
ok 3..... 2..... 1.. let's jam
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24 Jun 2004, 14:32
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#15
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Miles Teg
Join Date: Nov 2001
Location: Dom City
Posts: 5,192
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Re: Maths people, enlighten me
a+b+c...+z=>a+b+c+...d=>9
(if you make a 1 digit of it by calcing it, like 54=>9 and 99=>18=>9)
then abcd...z is divisionable by 9
__________________
Audentes Fortuna Iuvat
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24 Jun 2004, 14:38
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#16
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Registered User
Join Date: Jun 2000
Posts: 8,476
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Re: Maths people, enlighten me
"it's divisble by 9 iff the sum of the diigits is divisible by 9, assuming its an integer" would be an easier way of stating it.
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24 Jun 2004, 14:54
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#17
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Miles Teg
Join Date: Nov 2001
Location: Dom City
Posts: 5,192
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Re: Maths people, enlighten me
i suck at those things
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Audentes Fortuna Iuvat
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