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by MartianInvader
Sun Nov 11, 2007 4:18 pm UTC
Forum: Mathematics
Topic: weird question
Replies: 25
Views: 2571

Re: weird questin

I must admit, my least favorite part of math is differential equations.
by MartianInvader
Sat Nov 10, 2007 12:01 am UTC
Forum: Logic Puzzles
Topic: Helpful and Unhelpful (Solution thread)
Replies: 30
Views: 3677

Re: Helpful and Unhelpful (Solution thread)

I doubt that its provably impossible to figure out which door to go through, due to the not-well-defined nature of the word "Helpful". It seems you'd go in circles (Unhelpful will act just like Helpful, which means Helpful would act differently to distinguish himself, which means Unhelpful...
by MartianInvader
Sun Nov 04, 2007 9:22 pm UTC
Forum: Mathematics
Topic: Using Logs to Solve
Replies: 6
Views: 1287

Re: Using Logs to Solve

xlog(x)=log(x) x=1 Technically you can't even quite do this, since when you divide by log(x) you're assuming x isn't 1 (otherwise you're dividing by zero). So this actually shows a contradiction and proves that x can't be any positive number OTHER than 1, which you can then plug in and find that it...
by MartianInvader
Sun Nov 04, 2007 3:29 am UTC
Forum: Mathematics
Topic: Pi repeats and the uncountable infinite set of numbers...
Replies: 14
Views: 2082

Re: Pi repeats and the uncountable infinite set of numbers...

SimonM wrote:Depends on whether or not the digits are perfectly randomly distributed


It's an open question as to whether they are, but the first 10 trillion or so (all we've calculated) seem to be (assuming you're using a reasonable definition of "random").
by MartianInvader
Fri Nov 02, 2007 2:20 pm UTC
Forum: Mathematics
Topic: 2=1
Replies: 11
Views: 1696

Re: 2=1

Not sure if it's been done before so I'll just tack it onto this thread: 16 - 36 = 25 - 45----------------------------(Both are -20) 16 - 36 + 81/4 = 25 - 45 + 81/4----------(add 81/4 to each side) (4 - 9/2)^2 = (5 - 9/2)^2------------------(simplify the x^2 + 2xy + y^2 expressions) 4 - 9/2 = 5 - 9/...
by MartianInvader
Fri Nov 02, 2007 1:55 pm UTC
Forum: Mathematics
Topic: Geodesics: Donuts are Delicious
Replies: 10
Views: 1634

Re: Geodesics: Donuts are Delicious

Well, it depends what sort of metric you have on the torus, but I'll assume it's the standard one you get from identifying the sides of a square with sidelength 1. Try drawing 9 copies of this sqaure in a 3x3 pattern, and put your first point in the middle square. Now you can put 9 copies of your se...
by MartianInvader
Wed Oct 31, 2007 9:27 pm UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2429

Re: City Planning

Token wrote:Given that it was big enough to scare him into running an entire kilometer, I assume it was the penguin queen, who resides exactly at the South Pole.


Ah, but if it was the penguin queen at the South Pole, then he didn't run at all, now, did he?
by MartianInvader
Wed Oct 31, 2007 2:01 pm UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2429

Re: City Planning

Ok, I've changed the statement of the problem to be a bit less obvious. If anyone's curious, the math concept that inspired this was that of a Cayley Graph (wikipedia has a nice writeup on what these are). The problem is actually asking you to find the Cayley graph of the group with presentation <a,...
by MartianInvader
Wed Oct 31, 2007 12:13 am UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2429

Re: City Planning

Indeed. Hm, 3 answers in 15 minutes... I guess it was too easy with the sports thing, maybe I should have just left out the 4th condition and instead asked what familiar graph the streets make.

Anyhoo, well done!
by MartianInvader
Tue Oct 30, 2007 11:53 pm UTC
Forum: Logic Puzzles
Topic: City Planning
Replies: 19
Views: 2429

City Planning

Here's a puzzle inspired by (though not requiring) some rather hefty mathematics: A city planner is given some odd requirements by a rather eccentric governor for the city he's designing. There are 4 requirements: - Each street corner must have exactly 3 streets (not the usual 4). Of these streets, ...
by MartianInvader
Tue Oct 30, 2007 10:06 pm UTC
Forum: Forum Games
Topic: Count to 1 1000 times!
Replies: 1000
Views: 156259

Re: Count to 1 1000 times!

16836 rewritten in base 26
by MartianInvader
Tue Oct 30, 2007 8:11 pm UTC
Forum: Logic Puzzles
Topic: 10 Word Puzzles
Replies: 17
Views: 3131

Re: 10 Word Puzzles

Guess for 4.

Spoiler:
4. The types of US currency, from a penny to the $1000.00 bill? Including the golden dollar, so there's 12 faces even with the repeats of Washington and Lincoln.
by MartianInvader
Mon Oct 29, 2007 9:32 pm UTC
Forum: Logic Puzzles
Topic: Circles on a plane
Replies: 33
Views: 4022

Re: Circles on a plane

I'm not certain, but it seems to me that if you're talking about open circles, then the fractal-ish pattern would leave out points, but if you're talking about closed circles, then everything gets covered. Neither was specified at the start of the problem, so I was using closed circles. quintopia: Y...
by MartianInvader
Sun Oct 28, 2007 11:58 pm UTC
Forum: Mathematics
Topic: limit of a function defined in terms of another function
Replies: 18
Views: 2006

Re: limit of a function defined in terms of another function

Can't you interpolate a quadratic onto any 3 points? In particular, I think if you find the quadratic passing through (0, .5), (.5, .8 ), and (.8, .5), you'll get a quadratic function which satisfies the given conditions, but repeated applications of the function will keep oscillating between .5 and...
by MartianInvader
Sat Oct 27, 2007 6:21 pm UTC
Forum: General
Topic: INTRO THREAD THE THIRD
Replies: 10908
Views: 2095470

Re: POST HERE FIRST - INTRO THREAD THE THIRD

Hi, I'm a math grad student in the US. Stumbled onto xkcd a while ago and loved it (I really identified with a lot of the comics in the archives). I really liked the math and logic puzzles parts of these forums, and finally got around to registering today.
by MartianInvader
Sat Oct 27, 2007 6:12 pm UTC
Forum: Logic Puzzles
Topic: Circles on a plane
Replies: 33
Views: 4022

Re: Circles on a plane

I had to register just to comment on this. You never said all the circles had to be the same size. If they can get very small, you can cover the plane with a fractal-like pattern of circles so that each circle intersects only four others, and each point of the plane is contained in no more than two ...

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