My yummy tail is more delicious than apples.
1) Which arena has the second highest VD?
2) Which arena has the second lowest VD?
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Hint: Do not assume the conclusion. For example, "n is even" should not be anywhere except for the last line/sentence.
_____
Holo
Treasurer
ISML Seitokai
RESULTS: 2011 Diamond 7
 Chocola
 Hikarin's Kitty
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RESULTS: 2011 Diamond 7
A tall, towering wall looms in front of me. Beyond that is something that I could never to see on my own.
And that is...the view from the top.

 Incubator
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Re: RESULTS: 2011 Diamond 7
1. Arena 19
2. Arena 18
3. since p implies q (p>q)
let p be "2n²+5n12 is even"
let q be "n is even"
use proof by contradiction
Assume 2n²+5n12 is even but n is odd
since n is odd, 2n²+5n12 would be odd because 2n² is even, 5n is odd and 12 is even. odd + even + even = odd
which is a contradiction to the original statement so n is even
But there might be a twist to it. Holo is treasurer.
2. Arena 18
3. since p implies q (p>q)
let p be "2n²+5n12 is even"
let q be "n is even"
use proof by contradiction
Assume 2n²+5n12 is even but n is odd
since n is odd, 2n²+5n12 would be odd because 2n² is even, 5n is odd and 12 is even. odd + even + even = odd
which is a contradiction to the original statement so n is even
But there might be a twist to it. Holo is treasurer.
Last edited by xcrossfacekillahx on Mon Oct 03, 2011 9:32 am, edited 4 times in total.
 Bastion
 Titan
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Re: RESULTS: 2011 Diamond 7
1) Which arena has the second highest VD?
10: Goko Ruri vs Sakagami Tomoyo (top)
25: Holo vs Aisaka Taiga (2nd)
2) Which arena has the second lowest VD?
2: Shana vs Katsura Hinagiku (top)
17: Misaka Mikoto vs Tachibana Kanade (2nd)
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Assume n is even. You didn't state that the proof even needed to be mathmatical.
Edited to include the first two questions, the third question only got an underline to emphasize a piece of the statement.
Assuming is a usable method.
10: Goko Ruri vs Sakagami Tomoyo (top)
25: Holo vs Aisaka Taiga (2nd)
2) Which arena has the second lowest VD?
2: Shana vs Katsura Hinagiku (top)
17: Misaka Mikoto vs Tachibana Kanade (2nd)
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Assume n is even. You didn't state that the proof even needed to be mathmatical.
Edited to include the first two questions, the third question only got an underline to emphasize a piece of the statement.
Assuming is a usable method.
Last edited by Bastion on Mon Oct 03, 2011 8:46 pm, edited 2 times in total.
Jamie AB is open for business. How would you like your harebrained scheme?
Confusing statements are fun :p
http://i979.photobucket.com/albums/ae27 ... nner1.png" onclick="window.open(this.href);return false;[/img]
*Puts Nagi behind the drums and Hinagiku at the front with the mike and a guitar*
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Your sense of time tells you how much of your life has been wasted because you didn't take us at our word. ~Cracked.com
Never attribute to malice that which can be adequately explained by stupidity.
Azunyan, Hinachan, Aoyamachan and Subarunyanchan
Confusing statements are fun :p
(*'////'*)Medaka Kurokami wrote:People aren't meant to protect the rules, rules are meant to protect people
SpoilerShow
http://i979.photobucket.com/albums/ae27 ... nner1.png" onclick="window.open(this.href);return false;[/img]
*Puts Nagi behind the drums and Hinagiku at the front with the mike and a guitar*
Banners made by Midnight Jasper & Marinara
Kordosa wrote:I can just imagine all of the Hinagiku facepalming moments. That alone is worth it.
HnG chapter 333 pg 9 wrote:She (Hinagiku) realized an incredibly obvious but oft overlooked point: One had to read the manga before they could give their judgment of it.
ithekro wrote:Remember you aren't allowed to use your powers for evil.
With great power comes great responsibility
Absolute power corrupts absolutely
Tomoya Okazaki wrote:Can I beat you until you're motionless?
MegaTokyo wrote:Some of us are just a little more screwed up than others.
Saber (maglor) wrote:It is not how much, but it is where the king spends that tells what kind of king he is.
Rito wrote:Men don't decide whether they like someone or not based solely on breast size.
The lunatics around you are once again doing something to lower your opinion of human intelligence. ~Face PalmKordosa wrote:Boy, I really need to learn to keep my questions to myself. It only makes things worse.
Your sense of time tells you how much of your life has been wasted because you didn't take us at our word. ~Cracked.com
Never attribute to malice that which can be adequately explained by stupidity.
 Team Rocket Elite
 Moon princess
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Re: RESULTS: 2011 Diamond 7
1) Arena 19
2) Arena 18
3) Working on this
2) Arena 18
3) Working on this
A miracle that you believe in when you know it won't happen......... is hope.
 RegalStar
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Re: RESULTS: 2011 Diamond 7
1. 19
2. 21
3. The original equation = (2n3)(n+4). 2n is even and 3 is odd, so 2n3 is always odd. 4 is even, so if n is odd then n+4 is also odd, and (2n3)(n+4) would be odd. Thus, n must be even if (2n3)(n+4) is even.
Don't like roundabout answers but since I'm not the first one to the obvious, gotta come up with something else.
2. 21
3. The original equation = (2n3)(n+4). 2n is even and 3 is odd, so 2n3 is always odd. 4 is even, so if n is odd then n+4 is also odd, and (2n3)(n+4) would be odd. Thus, n must be even if (2n3)(n+4) is even.
Don't like roundabout answers but since I'm not the first one to the obvious, gotta come up with something else.
Last edited by RegalStar on Mon Oct 03, 2011 2:31 pm, edited 1 time in total.
 Yakuman
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Re: RESULTS: 2011 Diamond 7
1) Arena 19
2) Arena 21
3) Let's take this apart. 2n² translates to SnS which is an acronym to Shakugan no Shana. 5n refers to the n in Shana's name who is currently fifth on the chart. 12 is Shana's point difference to Kanade and Mikoto on the chart. If this monster is even that means exactly one or all three parts of this thing has to be even in order to be true.
Since the 'n' in SnS refers to 'no', a word with two letters, it is even. The second 'n' is the fourth letter in Shana's name, so it's also even. If we would remove the point difference between her and the leaders, she would end up second on the chart, since that would mean that she defated Mikoto (the chance for beating Tenshi is insignificant). Two is also an even number.
Here you go, I proved that if 2n²+5n12 is even then n is even too.
2) Arena 21
3) Let's take this apart. 2n² translates to SnS which is an acronym to Shakugan no Shana. 5n refers to the n in Shana's name who is currently fifth on the chart. 12 is Shana's point difference to Kanade and Mikoto on the chart. If this monster is even that means exactly one or all three parts of this thing has to be even in order to be true.
Since the 'n' in SnS refers to 'no', a word with two letters, it is even. The second 'n' is the fourth letter in Shana's name, so it's also even. If we would remove the point difference between her and the leaders, she would end up second on the chart, since that would mean that she defated Mikoto (the chance for beating Tenshi is insignificant). Two is also an even number.
Here you go, I proved that if 2n²+5n12 is even then n is even too.
Hurry up and make a contract with me! ◕‿‿◕
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defeated but not forgotten favoritesShow
 YagamiHayate
 Combat butler
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Re: RESULTS: 2011 Diamond 7
1) Arena 19
2) Arena 7
3)2n^{2}+5n12 factorised is (2n3)(n+4)
2n is even, so (2n3) is odd.
Odd*Even = Even, so (n+4) is even, therefore n is even.
Edit: I just realised this is exactly what RegalStar already did. Uhh, I can't be bothered thinking of another method.
2) Arena 7
3)
2n is even, so (2n3) is odd.
Odd*Even = Even, so (n+4) is even, therefore n is even.
Edit: I just realised this is exactly what RegalStar already did. Uhh, I can't be bothered thinking of another method.
 Alexander
 Translator
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Re: RESULTS: 2011 Diamond 7
1. Arena 19
2. Arena 18
2. Arena 18
WhateverShow
Given 2n²+5n12
We have that 12=Even
Assuming n=Odd
2n²=Even
5n=Odd
Even+OddEven=Odd
We have that 12=Even
Assuming n=Odd
2n²=Even
5n=Odd
Even+OddEven=Odd
Last edited by Alexander on Tue Oct 04, 2011 12:06 am, edited 1 time in total.
 Jeffreysama
 Soul gem
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Re: RESULTS: 2011 Diamond 7
1) Which arena has the second highest VD?
Arena 19
2) Which arena has the second lowest VD?
Arena 2
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Seriously... why math? ._."
And, xcrossfacekillahx took my contradiction answer (just when I thought calculus at school was going to be useful).
I'll try to expand on his proof.
Proof
Arena 19
2) Which arena has the second lowest VD?
Arena 2
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Seriously... why math? ._."
And, xcrossfacekillahx took my contradiction answer (just when I thought calculus at school was going to be useful).
I'll try to expand on his proof.
Proof
Code: Select all
Assume 2n² + 5n  12 is even.
Suppose n is odd.
Lemma 1: If n² is even, n is also even
Let n = 2k (even since any multiple of 2 is even)
n² = (2k)²
n² = 4k²
n² = 2(2k²) > even
Q.E.D.
By Lemma 1, n² is odd if n is odd.
Thus, 2n² is even.
Lemma 2: The product of two odd numbers is odd.
Let two odd numbers be (2n + 1) and (2m + 1)
Multiplying them together would result in:
(2n + 1)(2m + 1)
= 4nm + 2n + 2m + 1
= 2(2nm + n + m) + 1
> odd
Q.E.D.
By Lemma 2, 5n is odd.
Lemma 3: The sum of and even and odd number is odd.
Let an even number be 2n and an odd number be (2m + 1)
Adding them together would result in:
2n + 2m + 1
= 2(n + m) + 1
> odd
Q.E.D.
And so, 2n² + 5n  12 > even + odd  even.
By Lemma 3, 2n² + 5n  12 is odd.
> CONTRADICTION
Therefore, n must be even if 2n² + 5n  12 is even.
Q.E.D.
Last edited by Jeffreysama on Mon Oct 03, 2011 3:25 pm, edited 2 times in total.
 Eclairs
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Re: RESULTS: 2011 Diamond 7
Q1  2nd largest VD : Arena 25 [ Taiga X Holo ]
Q2  2nd closest match : Arena 17 [ Railgun x Kanade ]
Q3 
< edit 1 : copied the wrong equation, it was supposed to be 2n^2 + 5n  12, not 2n^2  5n + 12 : but the proof is still the same >
Q2  2nd closest match : Arena 17 [ Railgun x Kanade ]
Q3 
boring proof.Show
f(n) = 2n^2 + 5n  12  eq. 1
lets make a 2nd equation to define odd and even .
[ odd ] = 2x+1 , where infinity < x < infinity , x is an integer.  eq. 2
[ even ] = 2x , where infinity < x < infinity, x is an integer.  eq. 3
from the equation 1 : lets call 2n^2 = A . it can also be defined as 2x, where x = n^2, hence A is even  1st premise
: lets call 5n = B, we can the redefine B as 2*[2n] + n, and lets redefine 2n as N, this gives B a new equation of B = 2N + n
: lets call 12 = C, C can easily be defined from equation 2 as C = 2*[6] , hence C is even  2nd premise
From mathematics : [ even ]  [ even ] + [ even ] = [ even ] , [ even]  [ odd ] + [ even ] = [ odd ] = 2nd Premise
Proof : [2p]  [2q] + [ 2r] = 2[pq+r] and it satisfy equation 2, where [pq+r] = x
: [2k]+[2l+1] [2m] =2[k+lm] + 1 = 2[k+lm]+1 and satisfy equation 3, where [k+lm] = x
From the equation 1 ( simplified ) : A + B  C. For A + B  C to satisfy equation 2 : A, B and C must be [ even ], with A and C are already [even ] ,
We can the condense the proving into the B part.
B = 5n = 2[2n] + n = 2N + n. for B to be [ even ] , n must be [ even ], from the 2nd premise
lets make a 2nd equation to define odd and even .
[ odd ] = 2x+1 , where infinity < x < infinity , x is an integer.  eq. 2
[ even ] = 2x , where infinity < x < infinity, x is an integer.  eq. 3
from the equation 1 : lets call 2n^2 = A . it can also be defined as 2x, where x = n^2, hence A is even  1st premise
: lets call 5n = B, we can the redefine B as 2*[2n] + n, and lets redefine 2n as N, this gives B a new equation of B = 2N + n
: lets call 12 = C, C can easily be defined from equation 2 as C = 2*[6] , hence C is even  2nd premise
From mathematics : [ even ]  [ even ] + [ even ] = [ even ] , [ even]  [ odd ] + [ even ] = [ odd ] = 2nd Premise
Proof : [2p]  [2q] + [ 2r] = 2[pq+r] and it satisfy equation 2, where [pq+r] = x
: [2k]+[2l+1] [2m] =2[k+lm] + 1 = 2[k+lm]+1 and satisfy equation 3, where [k+lm] = x
From the equation 1 ( simplified ) : A + B  C. For A + B  C to satisfy equation 2 : A, B and C must be [ even ], with A and C are already [even ] ,
We can the condense the proving into the B part.
B = 5n = 2[2n] + n = 2N + n. for B to be [ even ] , n must be [ even ], from the 2nd premise
Last edited by Eclairs on Mon Oct 03, 2011 6:29 pm, edited 3 times in total.
Thanks a lot to HikariChan , MidnightJasper and ppizzapie for the awesome signatures and slivers. "Take caution thy children, for thou art guilty of sin if thou does not fappeth to the lolis!" Bob 23:29192
 fujibayashi
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Re: RESULTS: 2011 Diamond 7
1) Which arena has the second highest VD?
Arena 19
2) Which arena has the second lowest VD?
Arena 9
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
Arena 19
2) Which arena has the second lowest VD?
Arena 9
3) Let n be an integer. Prove that if 2n²+5n12 is even, then n must be even. Your proof can be in any method that makes sense as long as it's different from the preceding ones.
SpoilerShow
2n² must even.
Even12(even) =even.
If 2n²+5n12 is even,then 5n = even.
5 times even → even
So n=even.
Even12(even) =even.
If 2n²+5n12 is even,then 5n = even.
5 times even → even
So n=even.
 lihuazou
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Re: RESULTS: 2011 Diamond 7
1) Arena 19
2) Arena 18
3) Because 2n²+4n12 is even
2) Arena 18
3) Because 2n²+4n12 is even
Isml Data(20082013)http://pan.baidu.com/s/1qWxye40
 maglor
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Re: RESULTS: 2011 Diamond 7
@lihuazou : Next time, I think you should help KS and I grade these proofs.lihuazou wrote:1) Arena 19
2) Arena 18
3) Because 2n²+4n12 is even

 Cherry blossom
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Re: RESULTS: 2011 Diamond 7
I. Arena 25 (Holo/Taiga)
II. Arena 16 (Yui/Hitagi)
III. We know these things to be true:
1) even + odd = odd
2) even + even = even
3) odd + odd = even
4) odd * even = even
5) odd * odd = odd
6) even * even = even
2n²+5n12 (assume n is an integer)
2n² must be even, regardless of n's value. If n is odd, it's even * odd * odd, which must be even (#4). If n is even, it's even * even * even, which must be even (#6).
5n may be even or odd, depending on if n is odd. If n is odd, 5n is odd (#5). If n is even, 5n is even (#4).
12 is even.
We know that 2n² and 12 are even, so their sums must be even (#2). All that leaves unknown is the value of 5n.
If 5n is odd, then the equation is even + odd + even, which must be odd (#1). We also know that if 5n is odd, then n is odd (see earlier), so if 2n²+5n12 is odd, then n must be odd.
If 5n is even, then the equations is even + even + even, which must be even (#2). We also know that if 5n is even, then n is even (see earlier), so if 2n²+5n12 is even, then n must be even.
II. Arena 16 (Yui/Hitagi)
III. We know these things to be true:
1) even + odd = odd
2) even + even = even
3) odd + odd = even
4) odd * even = even
5) odd * odd = odd
6) even * even = even
2n²+5n12 (assume n is an integer)
2n² must be even, regardless of n's value. If n is odd, it's even * odd * odd, which must be even (#4). If n is even, it's even * even * even, which must be even (#6).
5n may be even or odd, depending on if n is odd. If n is odd, 5n is odd (#5). If n is even, 5n is even (#4).
12 is even.
We know that 2n² and 12 are even, so their sums must be even (#2). All that leaves unknown is the value of 5n.
If 5n is odd, then the equation is even + odd + even, which must be odd (#1). We also know that if 5n is odd, then n is odd (see earlier), so if 2n²+5n12 is odd, then n must be odd.
If 5n is even, then the equations is even + even + even, which must be even (#2). We also know that if 5n is even, then n is even (see earlier), so if 2n²+5n12 is even, then n must be even.
Stocking's gonna need to see your f*****' hands at the concert.
 Chocola
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Re: RESULTS: 2011 Diamond 7
@xcrossfacekillahx: simple and lovely
@RegalStar: Very good, just what I had in mind when I made it factorable. However, your sequence of proof should to be: (2n3)(n+4) is even, so (n+4) must be even since even/odd=even, and hence even4=even. Using division makes you not assume what n is first, although it will work if you clarify by breaking up into case 1: n is even, case 2: n is odd since they are disjoint.
@Alexander: The first part of your proof is all you need, because it's proving my contrapositive: assume n is odd and arrive at being odd. The second part of your proof is wrong because it assumes n is even so delete it.
@Eclairs: I'll let maglor handle this...
@fujibayashi: good and concise
@lihuazou: the easiest proof, although you might want to clarify n = 2n²4n+12 and the RHS is even.
@amdrag: maglor can handle this too...
Right now, everything simple has been taken except the contrapositive proof where you assume n = 2k+1 and arrive at 2n²+5n12 = 2(~)+1 after lots of algebra. If someone wants to try it go ahead.
@RegalStar: Very good, just what I had in mind when I made it factorable. However, your sequence of proof should to be: (2n3)(n+4) is even, so (n+4) must be even since even/odd=even, and hence even4=even. Using division makes you not assume what n is first, although it will work if you clarify by breaking up into case 1: n is even, case 2: n is odd since they are disjoint.
@Alexander: The first part of your proof is all you need, because it's proving my contrapositive: assume n is odd and arrive at being odd. The second part of your proof is wrong because it assumes n is even so delete it.
@Eclairs: I'll let maglor handle this...
@fujibayashi: good and concise
@lihuazou: the easiest proof, although you might want to clarify n = 2n²4n+12 and the RHS is even.
@amdrag: maglor can handle this too...
Right now, everything simple has been taken except the contrapositive proof where you assume n = 2k+1 and arrive at 2n²+5n12 = 2(~)+1 after lots of algebra. If someone wants to try it go ahead.
A tall, towering wall looms in front of me. Beyond that is something that I could never to see on my own.
And that is...the view from the top.
 Deathscyther
 Space pirate
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 BrawlRlz28
 Temple priestess
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Re: RESULTS: 2011 Diamond 7
1 Arena 5
2 Arena 18
3 Simple, if someone says its even, its most likely even. So N is even.....yeah I don't get it either.
2 Arena 18
3 Simple, if someone says its even, its most likely even. So N is even.....yeah I don't get it either.
 Momento10
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Re: RESULTS: 2011 Diamond 7
1. 1
2. 2
2. 2
 Natsumi
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 Samurai
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Re: RESULTS: 2011 Diamond 7
1.18
2.19
2.19