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math problem for you all
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Date: May 24th, 2015 12:16 PM Author: Yapping area doctorate Consider the usual x-y coordinate plane. Assign every point (ordered pair of real numbers) the letter A,B, or C. Prove there exist two points with the same letter that are 1 unit apart.
This problem has the advantage of being both easier and more interesting than the dumb combinatorics problems that one dude was posting. |
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Date: May 25th, 2015 12:23 AM Author: beta bossy field toilet seat I assign every point the letter A. All the integers are 1 unit apart from the next integer on each axis. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957987) |
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Date: May 25th, 2015 1:28 AM Author: Yapping area doctorate (lawyer) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958361) |
Date: May 24th, 2015 12:20 PM Author: puce shrine dopamine here's the solution
http://asciiartist.com/wp-content/uploads/2015/01/b6973011-7dff-4e7a-a648-e42fbcfae4b3.jpg
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Date: May 24th, 2015 12:35 PM Author: Jet vivacious abode (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954501) |
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Date: May 24th, 2015 12:33 PM Author: flickering half-breed lol @ "easier". hint or gtfo (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954488) |
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Date: May 24th, 2015 12:34 PM Author: elite roommate (low IQ) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954496) |
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Date: May 24th, 2015 12:37 PM Author: flickering half-breed (chink) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954511) |
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Date: May 24th, 2015 7:21 PM Author: bisexual resort (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956379) |
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Date: May 24th, 2015 6:00 PM Author: flickering half-breed Wait -- if I CONCEDE the statement is true does that count as if I proved it? We lawyers call this "stipulate" (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956042) |
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Date: May 24th, 2015 6:16 PM Author: Yapping area doctorate *STIPULATES the Riemann Hypothesis*
*wins $1,000,000* |
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Date: May 24th, 2015 9:05 PM Author: flickering half-breed ahhhhhhhhhhhhh, u see u mathematicians can learn a thing or 2 from us lawyers (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956894) |
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Date: May 24th, 2015 7:07 PM Author: multi-colored mahogany background story becky 1. What does "every point" mean? Do you mean "every coordinate pair with integral x and y", or do you mean "every coordinate pair with real x and y"? If the latter, LJL at this joke of a question. If the former, read on for a disproof.
2. Assuming you mean that, then the statement is false. If you define the set of A points as {(x,y)|(x+y)mod2=0} and B points as {(x,y)|(x+y)mod2=1} where x and y are integers, then there is no A point within 1 unit of another A, and there is no B unit within another B, and there is no C unit within another C since there are no C units.
Proof that there is no A point within 1 unit of another A:
Choose two points in A, n and m. n = (x1,y1), m=(x2,y2).
The distance between m and n = sqrt((x1-x2)^2+(y1-y2)^2)).
Assume these two points are within 1 unit of each other. Because by postulation x1,y1,x2,y2 are all integers, in order to be within 1 unit of each other, either x1=x2 and |y1-y2|=1 or y1=y2 and |x1-x2|=1. The proof of this is left as an exercise for the reader, but it's pretty fucking obvious, merely tedious. Now we defined A such that (x+y)mod2=0, so let's look at the first point, W/OLOG:
(x1+y1)mod2=0, and now do some substitution (x2+y1)mod2=0, and by a theorem of absolute value addition I don't wnat to prove here, (x2+(y2+1))mod2=0 x2mod2 + y2mod2 + 1mod2 = 0
By the same definition of A, we know
(x2+y2)mod2 = 0 x2mod2 + y2mod2 = 0
So combine those,
x2mod2 + y2mod2 + 1mod2 = x2mod2 + y2mod2
simplify
1mod2 = 0
1 = 0
This is a contradiction. The proof regarding two points in B is almost exactly the same and is left as an exercise for the reader. Accordingly, the theorem has been disproved.
In fact, you can generalize the opposite statement as a theorem in N dimensions:
For any set of N-dimensional points with integral components, you can assign these points with N different labels such that no two points with the same label have a distance <= 1 |
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Date: May 24th, 2015 7:15 PM Author: flickering half-breed He said "the usual coordinate plane". Pretty sure he means the set of ordered pairs of real numbers , not integers (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956343) |
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Date: May 24th, 2015 7:18 PM Author: flickering half-breed In response to your edit, why is it a joke of a question, Because it's very easy or very hard? (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956367) |
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Date: May 24th, 2015 7:21 PM Author: Histrionic deer antler some of this looks familiar (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956380) |
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Date: May 24th, 2015 11:48 PM Author: Coral idiotic genital piercing kitty This is awesome. Someone posts a question acting smart, then this dude comes along (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957785) |
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Date: May 25th, 2015 3:15 AM Author: flesh associate plaza Well, that's your opinion. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958761) |
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Date: May 24th, 2015 7:11 PM Author: Provocative mood just do draw three unit circles, bro (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956321) |
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Date: May 24th, 2015 7:16 PM Author: flickering half-breed (Guy who wrongly thinks he proved it) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956357) |
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Date: May 24th, 2015 8:58 PM Author: Provocative mood just do keep drawing circles qed. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956859) |
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Date: May 24th, 2015 9:04 PM Author: flickering half-breed tried that and still couldn't reach a contradiction. did i just not think hard enough? or are you dumb and/or full of shit? (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956889) |
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Date: May 24th, 2015 9:17 PM Author: Provocative mood i'm dumb, bc i thought the question was to prove that there are two points *less* than one unit apart with teh same label, which actually you can do with only 2 circles, like this:
make a circle around "A". all points in this circle must be either B or C points. wlog, choose a "B" point on the boundary of this circle. draw a circle around it. all points within this circle must be A or C points. but there is a region where the A circle and the B circle intersect. all points inside this region must be C points. but since they are all C points and they are in a continuous region where the max distance is less than one, there are two C points within distance 1. |
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Date: May 24th, 2015 9:25 PM Author: flickering half-breed cr. math can be a little bitch sometimes, like sharklasers (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956990) |
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Date: May 24th, 2015 9:22 PM Author: Provocative mood (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956974) |
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Date: May 24th, 2015 7:16 PM Author: bisexual resort (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956359) |
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Date: May 24th, 2015 7:21 PM Author: flickering half-breed Actually, every point has infinitely many points 1 away from it (a circle of radius 1) But most of the points on the circle aren't 1 away from each other |
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Date: May 24th, 2015 7:19 PM Author: Adulterous arrogant church pifgeonhole, final answer (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956372) |
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Date: May 24th, 2015 7:24 PM Author: flickering half-breed Don't be a faggot. If you know the answer post it Or did u just google the problem and the top result wa something aboout the pidgeonhole principle? |
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Date: May 24th, 2015 7:28 PM Author: Adulterous arrogant church no, I am a brilliant mathematician and I don't feel like playing your silly games (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956404) |
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Date: May 24th, 2015 10:29 PM Author: Yapping area doctorate looks like we're still without a proof. shame. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957270) |
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Date: May 24th, 2015 10:35 PM Author: flickering half-breed kill yourself (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957297) |
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Date: May 24th, 2015 10:37 PM Author: Yapping area doctorate this is literally a problem for 6th graders in Russia (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957304) |
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Date: May 24th, 2015 11:30 PM Author: fear-inspiring aquamarine prole filthpig am i a faggot if i say the regular name of this problem?
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Date: May 24th, 2015 11:32 PM Author: flickering half-breed no (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957695) |
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Date: May 24th, 2015 11:35 PM Author: fear-inspiring aquamarine prole filthpig it's kinda faggot bro. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957712) |
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Date: May 24th, 2015 11:37 PM Author: flickering half-breed obviously and, obviously so what's the problem called? |
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Date: May 24th, 2015 11:40 PM Author: flickering half-breed u edited twice the 1st thing u said was that he rephrased the problem so we wouldnt be able to google it the 2nd thing u said was that nobody on this shitsite would be able to solve it |
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Date: May 24th, 2015 11:52 PM Author: Coral idiotic genital piercing kitty Mathbro here. gonna hit this question. So this means every point is randomly assigned a A,b or c? (Every unit could be A?) also, do you count diagnolly as one unit or what (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957797) |
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Date: May 24th, 2015 11:54 PM Author: flickering half-breed lol to be honest u dont sound like a math bro rephrase you're questions more coherently & i'll be happy 2 answer them |
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Date: May 25th, 2015 12:41 AM Author: Coral idiotic genital piercing kitty Ok. So you want us to prove that 1,1 and 2,1 (etc) can both be A? And each point is randomized between A, B, and C? (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958105) |
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Date: May 25th, 2015 1:26 AM Author: flickering half-breed stfu (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958346) |
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Date: May 25th, 2015 1:27 AM Author: Yapping area doctorate You need to show the statement holds for any assignment of letters.
And yes, 1 unit in any direction counts. |
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Date: May 25th, 2015 1:28 AM Author: flickering half-breed he's flaming, like u (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958358) |
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Date: May 25th, 2015 1:28 AM Author: Yapping area doctorate how am I flaming (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958363) |
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Date: May 25th, 2015 1:29 AM Author: Yapping area doctorate do you mean the gay kind of flaming or the lying kind (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958369) |
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Date: May 25th, 2015 1:51 AM Author: Violet den son of senegal The gay kind. See: this thread (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958467) |
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Date: May 25th, 2015 2:02 AM Author: elite roommate (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958498) |
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Date: May 25th, 2015 2:11 AM Author: Coral idiotic genital piercing kitty They can touch diagonally (sqrt 2???)? This is so stupid
Put A at 0,0. Theres 8 spots away that 0,0 can touch. Theres no way you can B and C in those spots without any touching eachother
Did i fuck up
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Date: May 25th, 2015 2:48 AM Author: Yapping area doctorate sqrt(2) is not equal to 1, bro.
(Also, because I don't think I made this clear, you're considering all points in the plane, not just those with integer coordinates.) |
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Date: May 25th, 2015 2:59 AM Author: Coral idiotic genital piercing kitty Ya just saw the thing below. Same shit. Just substitute a rombus for square, its all the same thing
Interesting shit tho I like these questions |
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Date: May 25th, 2015 2:53 AM Author: flickering half-breed found it, u little shit http://www.cut-the-knot.org/proofs/three_colors.shtml |
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Date: May 25th, 2015 2:54 AM Author: Yapping area doctorate it's kind of embarrassing you couldn't find that solution and apparently spent a lot of time Googling for it instead. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958694) |
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Date: May 25th, 2015 3:05 AM Author: flickering half-breed like u could solve that shit. oc if i were a shitflamer like u i would have proudly presented "my" solution (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958718) |
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Date: May 25th, 2015 3:09 AM Author: Yapping area doctorate I was a math major so ... yes I could. And id.
Should I post another problem thread? It won't be Googleable this time. |
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Date: May 25th, 2015 3:13 AM Author: Coral idiotic genital piercing kitty Do ittttttt hit us with one.
Wanna go 2/2 before i pass out |
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Date: May 25th, 2015 3:15 AM Author: Sable pit I solved it but can't put it into words (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958762) |
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Date: May 25th, 2015 5:04 AM Author: Sable pit okay I hadn't solved it but I have now. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958939) |
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Date: May 25th, 2015 3:15 AM Author: Ruby excitant state really tough guy (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958763) |
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Date: May 25th, 2015 3:18 AM Author: Coral idiotic genital piercing kitty Yo they all gotta be the same length my dude (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958770) |
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Date: May 25th, 2015 3:21 AM Author: Ruby excitant state really tough guy I know that, there was an error in my "proof", and I think to fix it, it becomes basically one of the solutions posted above (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958776) |