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math problem for you all
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Date: May 24th, 2015 12:16 PM Author: cerebral brethren 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: Fear-inspiring garrison 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: cerebral brethren (lawyer) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958361) |
Date: May 24th, 2015 12:20 PM Author: Dashing sound barrier 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: Lemon coldplay fan plaza (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: Wild Range Prole 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: Concupiscible maize athletic conference box office (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: Wild Range Prole (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: Outnumbered gold multi-billionaire native (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: Wild Range Prole 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: cerebral brethren *STIPULATES the Riemann Hypothesis*
*wins $1,000,000* |
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Date: May 24th, 2015 9:05 PM Author: Wild Range Prole 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: red faggotry gunner 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: Wild Range Prole 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: Wild Range Prole 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: Lime mentally impaired stead 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: flesh comical sex offender giraffe 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: flushed hall elastic band 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: Elite Locale Sneaky Criminal 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: Wild Range Prole (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: Elite Locale Sneaky Criminal 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: Wild Range Prole 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: Elite Locale Sneaky Criminal 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: Wild Range Prole 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: Elite Locale Sneaky Criminal (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: Outnumbered gold multi-billionaire native (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: Wild Range Prole 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: honey-headed stirring parlor azn 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: Wild Range Prole 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: honey-headed stirring parlor azn 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: cerebral brethren 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: Wild Range Prole 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: cerebral brethren 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: crimson mental disorder church 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: Wild Range Prole 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: crimson mental disorder church 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: Wild Range Prole obviously and, obviously so what's the problem called? |
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Date: May 24th, 2015 11:40 PM Author: Wild Range Prole 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: flesh comical sex offender giraffe 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: Wild Range Prole 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: flesh comical sex offender giraffe 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: Wild Range Prole 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: cerebral brethren 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: Wild Range Prole 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: cerebral brethren 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: cerebral brethren 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: soul-stirring saffron fortuitous meteor quadroon 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: Concupiscible maize athletic conference box office (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: flesh comical sex offender giraffe 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: cerebral brethren 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: flesh comical sex offender giraffe 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: Wild Range Prole 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: cerebral brethren 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: Wild Range Prole 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: cerebral brethren 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: flesh comical sex offender giraffe 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: Frisky Tank Cumskin 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: Frisky Tank Cumskin 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: indigo national security agency liquid oxygen (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: flesh comical sex offender giraffe 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: indigo national security agency liquid oxygen 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) |