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Home » Mathematics » Middle School Contests (MATHCOUNTS, AMC 8, MOEMS, Ages 10-13)
 
Mathcounts Challenge: Integers N
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Syntax Error
Navier-Stokes Equations
Navier-Stokes Equations

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#1
Mathcounts Challenge: Integers N
How many integers, n, can be written as a+b+c where a, b, and c are distinct odd integers between 2 and 20?
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PostPosted: Sun Sep 07, 2003 3:25 pm  Back to top 
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Tare
Navier-Stokes Equations
Navier-Stokes Equations

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#2
I really ought to learn C stuff...
I'm guessing the answer is Click to reveal hidden content
84
by brute force, but I'm not sure.
Last edited by Tare on Sun Sep 07, 2003 3:47 pm; edited 1 time in total 
PostPosted: Sun Sep 07, 2003 3:45 pm  Back to top 
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Fierytycoon
Navier-Stokes Equations
Navier-Stokes Equations

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#3
Quote:
I really ought to learn C stuff...


This is a math problem, not a programming problem.
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PostPosted: Sun Sep 07, 2003 3:46 pm  Back to top 
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Tare
Navier-Stokes Equations
Navier-Stokes Equations

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#4
Fierytycoon wrote:
Quote:
I really ought to learn C stuff...


This is a math problem, not a programming problem.

The other C (the "chooses" one)

PostPosted: Sun Sep 07, 2003 3:47 pm  Back to top 
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MysticTerminator
Birch & Swinnerton Dyer
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#5
nope, this has nothing to do with combinatorics. it's a bit simpler...

PostPosted: Sun Sep 07, 2003 3:48 pm  Back to top 
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Fierytycoon
Navier-Stokes Equations
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#6
Yeah, no combinatorics needed, just use logic.
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PostPosted: Sun Sep 07, 2003 3:51 pm  Back to top 
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Tare
Navier-Stokes Equations
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#7
well isn't it the combination of Click to reveal hidden content
a, b, and c within the set S={3,5,7,9,11,13,15,17,19}?

PostPosted: Sun Sep 07, 2003 3:53 pm  Back to top 
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MysticTerminator
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#8
Tare...your answer is a bit large. Perhaps you would like to explain your solution...

PostPosted: Sun Sep 07, 2003 3:53 pm  Back to top 
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Tare
Navier-Stokes Equations
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#9
Well Click to reveal hidden content
I figured since there's 9 numbers the solution would be 7*1+6*2+5*3+4*4+3*5+2*6+1*7 or 7(7+1)/2+6(6+1)/2+...+2(2+1)/2+1(1+1)/2 which should equal 84...maybe Smile


PostPosted: Sun Sep 07, 2003 3:57 pm  Back to top 
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TheSouthpaw
Riemann Hypothesis
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#10
Click to reveal hidden content


19 is the answer

The smallest is 15, the biggest is 51, and im willing to bet you can get everything in between



PostPosted: Sun Sep 07, 2003 4:25 pm  Back to top 
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MysticTerminator
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#11
yes, mr. southpaw, you are correct, although Click to reveal hidden content
i think you meant you could get any odd number in between

PostPosted: Sun Sep 07, 2003 4:29 pm  Back to top 
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TheSouthpaw
Riemann Hypothesis
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#12
Details, details.

PostPosted: Sun Sep 07, 2003 4:30 pm  Back to top 
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MysticTerminator
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#13
Tare wrote:
well isn't it the combination of Click to reveal hidden content
a, b, and c within the set S={3,5,7,9,11,13,15,17,19}?


tare...the reason this is incorrect is because Click to reveal hidden content
you are counting some possibilities more than once. for example, you count both 3+7+11 and 5+7+9 while they are in fact the same thing

PostPosted: Sun Sep 07, 2003 4:31 pm  Back to top 
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Tare
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#14
Ooooooh, I see. Swo hroiw dtied hye goeut trhpe arnoscweesrs again?! *interlacing subliminal message* Smile

PostPosted: Sun Sep 07, 2003 4:35 pm  Back to top 
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MysticTerminator
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#15
Tare wrote:
Ooooooh, I see. Swo hroiw dtied hye goeut trhpe arnoscweesrs again?! *interlacing subliminal message* Smile


Tare...you're supposed to be a moderator.

PostPosted: Sun Sep 07, 2003 4:38 pm  Back to top 
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Tare
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#16
*sigh* I know, I'm actually doing my job. I mean, I wanted to say "WRITE OUT THE PROCESS FOR THE LAST TIME!!!" but that would sound too harsh.

PostPosted: Sun Sep 07, 2003 4:40 pm  Back to top 
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Barnacle
Riemann Hypothesis
Riemann Hypothesis

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#17
15 to 51.. 19 odd integers and you can generate all by shifting by two's when necessary [why? Mr. Green ]

PostPosted: Fri Jun 17, 2005 8:24 pm  Back to top 
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