The most prestigious law school admissions discussion board in the world.
|
 |
 
|
math problem for you all
Poast new message in this thread
Date: May 24th, 2015 12:16 PM Author: spectacular kitty stage 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. |
 |
Date: May 25th, 2015 12:23 AM Author: Painfully Honest Boiling Water Rigpig 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) |
|
Date: May 25th, 2015 1:28 AM Author: spectacular kitty stage (lawyer) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958361) |
Date: May 24th, 2015 12:20 PM Author: chocolate cowardly sanctuary here's the solution
http://asciiartist.com/wp-content/uploads/2015/01/b6973011-7dff-4e7a-a648-e42fbcfae4b3.jpg
|
|
Date: May 24th, 2015 12:35 PM Author: Adventurous internet-worthy striped hyena (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954501) |
|
Date: May 24th, 2015 12:33 PM Author: Flushed Underhanded Station lol @ "easier". hint or gtfo (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954488) |
|
Date: May 24th, 2015 12:34 PM Author: crusty old irish cottage (low IQ) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954496) |
|
Date: May 24th, 2015 12:37 PM Author: Flushed Underhanded Station (chink) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27954511) |
|
Date: May 24th, 2015 7:21 PM Author: thriller knife den (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956379) |
|
Date: May 24th, 2015 6:00 PM Author: Flushed Underhanded Station 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) |
|
Date: May 24th, 2015 6:16 PM Author: spectacular kitty stage *STIPULATES the Riemann Hypothesis*
*wins $1,000,000* |
|
Date: May 24th, 2015 9:05 PM Author: Flushed Underhanded Station 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) |
|
Date: May 24th, 2015 7:07 PM Author: chartreuse school alpha 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 |
|
Date: May 24th, 2015 7:15 PM Author: Flushed Underhanded Station 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) |
|
Date: May 24th, 2015 7:18 PM Author: Flushed Underhanded Station 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) |
|
Date: May 24th, 2015 7:21 PM Author: brindle galvanic corner some of this looks familiar (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956380) |
|
Date: May 24th, 2015 11:48 PM Author: fear-inspiring charismatic site 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) |
|
Date: May 25th, 2015 3:15 AM Author: floppy spot Well, that's your opinion. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958761) |
|
Date: May 24th, 2015 7:11 PM Author: Big antidepressant drug just do draw three unit circles, bro (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956321) |
|
Date: May 24th, 2015 7:16 PM Author: Flushed Underhanded Station (Guy who wrongly thinks he proved it) (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956357) |
|
Date: May 24th, 2015 8:58 PM Author: Big antidepressant drug just do keep drawing circles qed. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956859) |
|
Date: May 24th, 2015 9:04 PM Author: Flushed Underhanded Station 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) |
|
Date: May 24th, 2015 9:17 PM Author: Big antidepressant drug 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. |
|
Date: May 24th, 2015 9:25 PM Author: Flushed Underhanded Station cr. math can be a little bitch sometimes, like sharklasers (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956990) |
|
Date: May 24th, 2015 9:22 PM Author: Big antidepressant drug (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956974) |
|
Date: May 24th, 2015 7:16 PM Author: thriller knife den (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956359) |
|
Date: May 24th, 2015 7:21 PM Author: Flushed Underhanded Station 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 |
|
Date: May 24th, 2015 7:19 PM Author: Swashbuckling Hall Famous Landscape Painting pifgeonhole, final answer (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27956372) |
|
Date: May 24th, 2015 7:24 PM Author: Flushed Underhanded Station 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? |
|
Date: May 24th, 2015 7:28 PM Author: Swashbuckling Hall Famous Landscape Painting 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) |
|
Date: May 24th, 2015 10:29 PM Author: spectacular kitty stage looks like we're still without a proof. shame. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957270) |
|
Date: May 24th, 2015 10:35 PM Author: Flushed Underhanded Station kill yourself (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957297) |
|
Date: May 24th, 2015 10:37 PM Author: spectacular kitty stage this is literally a problem for 6th graders in Russia (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957304) |
|
Date: May 24th, 2015 11:30 PM Author: blue stirring legend am i a faggot if i say the regular name of this problem?
|
|
Date: May 24th, 2015 11:32 PM Author: Flushed Underhanded Station no (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957695) |
|
Date: May 24th, 2015 11:35 PM Author: blue stirring legend it's kinda faggot bro. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27957712) |
|
Date: May 24th, 2015 11:37 PM Author: Flushed Underhanded Station obviously and, obviously so what's the problem called? |
|
Date: May 24th, 2015 11:40 PM Author: Flushed Underhanded Station 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 |
|
Date: May 24th, 2015 11:52 PM Author: fear-inspiring charismatic site 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) |
|
Date: May 24th, 2015 11:54 PM Author: Flushed Underhanded Station lol to be honest u dont sound like a math bro rephrase you're questions more coherently & i'll be happy 2 answer them |
|
Date: May 25th, 2015 12:41 AM Author: fear-inspiring charismatic site 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) |
|
Date: May 25th, 2015 1:26 AM Author: Flushed Underhanded Station stfu (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958346) |
|
Date: May 25th, 2015 1:27 AM Author: spectacular kitty stage You need to show the statement holds for any assignment of letters.
And yes, 1 unit in any direction counts. |
|
Date: May 25th, 2015 1:28 AM Author: Flushed Underhanded Station he's flaming, like u (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958358) |
|
Date: May 25th, 2015 1:28 AM Author: spectacular kitty stage how am I flaming (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958363) |
|
Date: May 25th, 2015 1:29 AM Author: spectacular kitty stage 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) |
|
Date: May 25th, 2015 1:51 AM Author: Khaki theatre The gay kind. See: this thread (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958467) |
|
Date: May 25th, 2015 2:02 AM Author: crusty old irish cottage (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958498) |
|
Date: May 25th, 2015 2:11 AM Author: fear-inspiring charismatic site 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
|
|
Date: May 25th, 2015 2:48 AM Author: spectacular kitty stage 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.) |
|
Date: May 25th, 2015 2:59 AM Author: fear-inspiring charismatic site 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 |
|
Date: May 25th, 2015 2:53 AM Author: Flushed Underhanded Station found it, u little shit http://www.cut-the-knot.org/proofs/three_colors.shtml |
|
Date: May 25th, 2015 2:54 AM Author: spectacular kitty stage 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) |
|
Date: May 25th, 2015 3:05 AM Author: Flushed Underhanded Station 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) |
|
Date: May 25th, 2015 3:09 AM Author: spectacular kitty stage I was a math major so ... yes I could. And id.
Should I post another problem thread? It won't be Googleable this time. |
|
Date: May 25th, 2015 3:13 AM Author: fear-inspiring charismatic site Do ittttttt hit us with one.
Wanna go 2/2 before i pass out |
|
Date: May 25th, 2015 3:15 AM Author: Razzle-dazzle national I solved it but can't put it into words (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958762) |
|
Date: May 25th, 2015 5:04 AM Author: Razzle-dazzle national okay I hadn't solved it but I have now. (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958939) |
|
Date: May 25th, 2015 3:15 AM Author: Pink tripping quadroon macaca (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958763) |
|
Date: May 25th, 2015 3:18 AM Author: fear-inspiring charismatic site Yo they all gotta be the same length my dude (http://www.autoadmit.com/thread.php?thread_id=2888104&forum_id=2#27958770) |
|
Date: May 25th, 2015 3:21 AM Author: Pink tripping quadroon macaca 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) |