## Search found 156 matches

Fri Jun 13, 2008 6:17 pm UTC
Forum: Mathematics
Topic: Maths Problem - Weights
Replies: 16
Views: 1657

### Re: Maths Problem - Weights

If the weights are badly chosen, there are fewer weight values that can be measured. Prove that this means that there is an arrangement of (some of) the weights in the two pans such that the scales balance. This is not the case. If the weights are 1, 2, 4, 8, 16, 32, 64, and 3153, then there's no w...
Fri Jun 13, 2008 6:08 pm UTC
Forum: Science
Topic: How many ways can you empty a glass of water?
Replies: 129
Views: 13199

### Re: How many ways can you empty a glass of water?

Put the glass in a microwave. Superheating for the win!
Fri Jun 13, 2008 6:05 pm UTC
Topic: 0436: "How It Happened"
Replies: 168
Views: 38833

### Re: "How It Happened" Discussion

It was enjoyable, I suppose. I'm not a big fan of the repetition, this technique has been used a little too often for it to be really considered as one of the best. All-in-all, disappointing. To be fair, I did chuckle a little bit. The position of the fingers was probably the best part.
Fri Jun 13, 2008 4:27 am UTC
Forum: Forum Games
Topic: Ban the person above you
Replies: 20286
Views: 1228763

### Re: Ban the person above you

Banned for wanting a bicycle.
Fri Jun 13, 2008 4:09 am UTC
Forum: Forum Games
Topic: Maximize the post:views ratio! (if you look, you must post)
Replies: 36982
Views: 2511070

### Re: Maximize the post:views ratio! (if you look, you must post)

And of course I just clicked "view the post you just made" or whatever, so now I need a new post for the new view... ><
Fri Jun 13, 2008 4:08 am UTC
Forum: Forum Games
Topic: Maximize the post:views ratio! (if you look, you must post)
Replies: 36982
Views: 2511070

### Re: Maximize the post:views ratio! (if you look, you must post)

If enough people look and post, we can at least bring the ratio up.

Its pretty unfortunate how many people would look and not post though. This isn't a very interesting thread.
Fri Jun 13, 2008 3:02 am UTC
Forum: Logic Puzzles
Topic: Figuring out what a function is.
Replies: 17
Views: 2556

### Re: Figuring out what a function is.

"Do you have enough information to determine it without a shred of doubt".... well, no. "Do you have enough information to guess", probably. In fact... Looking at the following sequences: 1@0, 1@1, 1@2, 1@3... = -1, -1, -1, -1... 2@0, 2@1, 2@2, 2@3... = -2, -1, 0, 1... 3@0, 3@1, ...
Tue Jun 10, 2008 3:31 am UTC
Forum: Mathematics
Topic: Orbit Stability
Replies: 26
Views: 3058

### Re: Orbit Stability

I was actually just thinking about this problem! I think the issue with "no mass" (I think somebody might have said this already) is to prevent the third particle from pulling at the first two. In other words, I think its fine to talk about two "fixed" particles of mass M and dis...
Fri Jun 06, 2008 1:07 am UTC
Forum: Logic Puzzles
Topic: Loot Distribution
Replies: 6
Views: 1700

### Re: Loot Distribution

Things get a little more fun if a proposal needs strictly more than a 50% vote to pass. Let's see how much more fun... We see that one person will automatically get all the money (obviously). With two people, all the second person can do to hope to stay alive is give all the money to person...
Thu Jun 05, 2008 9:28 pm UTC
Forum: Mathematics
Topic: Finding the Length of a Parabola
Replies: 18
Views: 2258

### Re: Finding the Length of a Parabola

Your sentiment is admirable, but it's clear you haven't tried to do this problem. The limit you're effectively asking the OP to take (without calculus) is the limit of \frac{2}{n} \sum_{j=1}^{n} \sqrt{1+((2j-1)/n)^2} , which is pretty hard even with calculus! Hard to exactly, maybe,...
Tue Jun 03, 2008 5:20 am UTC
Forum: Science
Topic: Physics Version 2.1.2
Replies: 44
Views: 6033

### Re: Physics Version 2.1.2

Removed bugs in which light acts like a particle instead of a wave. Added General Relativity 2.0- now fully compatible with Quantum Mechanics. All pullies are now frictionless and massless. The acceleration of gravity now equals exactly 10 m/s^2. Everywhere. Note; to differentiate this from the prev...
Tue Jun 03, 2008 4:50 am UTC
Forum: Science
Topic: How many ways can you empty a glass of water?
Replies: 129
Views: 13199

### Re: How many ways can you empty a glass of water?

In soviet russia, glass of water empties you!
Tue Jun 03, 2008 3:52 am UTC
Forum: Mathematics
Topic: Combining estimated probabilities
Replies: 10
Views: 1476

### Re: Combining estimated probabilities

Hm. My intuition here, though I'm not sure exactly how to explain why its fair, is the following: Eliezer thinks he has 20% chance of owning the bill, Nick believes 15%. Then we say the probability Eliezer actually owns the bill is proportional to the probability he thinks he owns it (20%) a...
Fri May 16, 2008 1:34 am UTC
Forum: Logic Puzzles
Topic: Hofstadter's Law and Byrd's Laws
Replies: 30
Views: 3945

### Re: Hofstadter's Law and Byrd's Laws

My thoughts on the matter: Looking at the theorems, it seems like they are all equivalent to each other, and to: A = "It always takes longer than you think it will take" The "even if" is a (mostly humerous, it seems) clarification. But the "always" in the statem...
Thu May 08, 2008 2:35 am UTC
Forum: Mathematics
Replies: 3
Views: 1632

Start with a point on such a graph. Move along an edge to another vertex. At the other vertex, there will always be another edge coming out of that vertex. Travel that edge to the other vertex. At your new vertex, there will similarly be a new edge to travel, etc, etc, until you return to your origi...
Thu May 08, 2008 2:23 am UTC
Forum: Mathematics
Topic: An oddity...
Replies: 17
Views: 3601

### Re: An oddity...

Its not hard to show f(n) < n for all n greater than 999. Suppose 1000^k <= n < 1000^(k+1) for some integer k. Then n has k+1 distinct blocks of three digits (the last block may have less than 3 digits). For example, let n = 56,723,456. Then 1000^2 < n < 1000^3, and n has 3 "blocks" of 3 d...
Mon Apr 28, 2008 4:45 am UTC
Forum: General
Topic: A Softer World: 299 - Mention of XKCD
Replies: 13
Views: 3687

### Re: A Softer World: 299 - Mention of XKCD

I was just about to link to 289... I think that one is much more clearly a xkcd ref. But maybe this one is too?
Wed Apr 23, 2008 5:50 am UTC
Topic: 0413: "Mistranslations"
Replies: 110
Views: 21792

### Re: "Mistranslations" Discussion

Absolutely brilliant. The perfect mix of romance and absurdity!

I am interested to see how this particular scene unfolds...
Mon Apr 21, 2008 5:37 am UTC
Forum: Logic Puzzles
Topic: Recognize this sequence?
Replies: 36
Views: 9147

### Re: Recognize this sequence?

Note that the numbers in the sequence are equal to a^2*b^2 where a/b is a good approximation of the square root of 2. To look again at the sequence: a1 = 1^2*1^2 a2 = 3^2*2^2 a3 = 7^2*5^2 a4 = 17^2*12^2 etc. In other words, a^2 = 2*b^2 +/- 1. We can show this by induction, using the proposed recurs...
Sun Apr 20, 2008 7:16 pm UTC
Forum: Mathematics
Topic: Vectors
Replies: 12
Views: 2310

### Re: Vectors

That looks right! Here are some hints to get you started: If you call the vector from O to P vector c, you might be able to set up a system that you can solve for c in terms of a and b. How can you talk about the vector from A to B in terms of a, b and c? How about the vector from P to A? From P to ...
Sat Apr 19, 2008 5:48 am UTC
Topic: 0412: "Startled"
Replies: 127
Views: 33292

### Re: "Startled" Discussion

Evidence against it being a BHM/BHG add-on: its title isn't "journal 4" and, as people have pointed out, the girl has shorter hair. Also, the story is very surreal by itself, and even more so when we try to reconcile it with the previous elements of the story. (BHM has a crush? She now wan...
Tue Apr 15, 2008 11:23 pm UTC
Forum: Mathematics
Topic: Question from this year's Euclid
Replies: 3
Views: 1078

### Re: Question from this year's Euclid

Spoilered: Take the natural logarithm of both sides. Using ln(a*b) = ln(a) + ln(b) and the fact that ln(a^x) = x*ln(a), we get: (x+2)*ln(2) + (6-x)*ln(5) = x^2*ln(2) + x^2*ln(5) Subtracting and factoring: (x^...
Thu Apr 10, 2008 1:49 am UTC
Forum: Logic Puzzles
Topic: 3 door problem
Replies: 88
Views: 29536

### Re: 3 door problem

poohat: I may have been ambiguous on this point, but it was always my intention (as in the original Monty Hall problem) that the host ALWAYS picks a box/door that he knows for sure does not have the prize. The variance comes depending on if he can open boxes you have already picked (ie you pick box ...
Thu Apr 10, 2008 1:04 am UTC
Forum: Mathematics
Topic: another math problem for my game
Replies: 5
Views: 1469

### Re: another math problem for my game

Fortunately for you, the angle d (if I understand the picture correctly) is congruent to angle t!
Sun Apr 06, 2008 5:10 am UTC
Forum: Mathematics
Topic: two-one function
Replies: 41
Views: 5192

### Re: two-one function

For each i, the restriction f|Ui of f to Ui is continuous and assigns at most two x values to any single y value. Such a continuous function can have at most one local maximum, and at most one local minimum... I'm basically convinced that this is true, I'm just wary because there are plenty of &quo...
Tue Apr 01, 2008 10:40 pm UTC
Forum: Forum Games
Replies: 17
Views: 2797

### Re: (Reverse) Google search challenge

Er... is there some kind of honor system saying that you shouldn't actually use google to figure this out? Cause a search in quotes of any of the results basically gives you the answer right away. Example: googling "America's Pretzel Bakery" gives the answer to the previous challenge, whic...
Tue Apr 01, 2008 10:12 pm UTC
Forum: General
Topic: April Fools (WE KNOW ABOUT THE QC THING KTHX)
Replies: 136
Views: 21728

### Re: April Fools (WE KNOW ABOUT THE QC THING KTHX)

I was just about to say, this topic is gonna be a whole lot easier to read when they remove the filter (presumably tomorrow). So many posts that look like:

"I clicked on Questionable Content and got Questionable Content! Oh me yarm! I was freakin out!"
Tue Apr 01, 2008 1:07 am UTC
Forum: Logic Puzzles
Topic: 3 door problem
Replies: 88
Views: 29536

### Re: 3 door problem

Yep, sorry for being unclear. My intention was that he cannot pick a box you've already picked, but I agree with the answer for both sets of rules.
Sat Mar 29, 2008 1:20 am UTC
Forum: Logic Puzzles
Topic: 3 door problem
Replies: 88
Views: 29536

### Re: 3 door problem

A common explanation for the solution to this problem is: "Since I have 1/3 chance of picking the prize box initially, then once I pick the box I have 1/3 chance of getting the prize and there is 2/3 chance that its in the remaining boxes. That doesn't change when the host reveals a box." ...
Sat Mar 29, 2008 12:53 am UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 424896

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

I think the best way to see why the guru gives information to the people (and his has been stated before) is to consider only two people with blue eyes. Then it is STILL true that each person sees somebody with blue eyes. And when the guru says to the town "I see somebody with blue eyes", ...
Thu Mar 27, 2008 6:04 am UTC
Forum: Mathematics
Topic: having trouble with two proofs
Replies: 38
Views: 2750

### Re: having trouble with two proofs

Defining the gcd as: "-a positive integer d is the greatest common divisor of integers a and b provided that i)d|a and d|b ii)if c|a and c|b then c|d" I would not say that's a great definition. For starters, how can we guarantee such a d exists? In fact, showing that this definition is val...
Tue Mar 04, 2008 4:50 am UTC
Forum: Logic Puzzles
Topic: Pitchers
Replies: 9
Views: 2728

### Re: Pitchers

How about: 4, 7, 10, divide the 10 into equal parts. Or: given 3 pitchers with volumes 3, 9, 11, the 11 initially filled. Demonstrate how to leave exactly k liters in the 11 liter pitcher, with 0 <= k <= 11. (And try to do it in the least number of moves possible) (I don't know if this is possible f...
Mon Mar 03, 2008 11:41 pm UTC
Forum: Mathematics
Topic: Solving Differential Equations
Replies: 13
Views: 1685

### Re: Solving Differential Equations

Also in response to Nimblefinger... mathmagic showed how to get from the original equation to: P'(x) - 2xP(x) = x*(x^2-a^2)(x^2-b^2) = x^5 - (a^2 + b^2)*x^3 + (a^2+b^2)*x From here, we can see P(x) must be a 4th degree polynomial: P(x&#...
Sun Mar 02, 2008 10:59 pm UTC
Forum: Mathematics
Topic: Summing of digits in numbers
Replies: 19
Views: 3771

### Re: Summing of digits in numbers

If you have n s-sided dice and want to roll k, the number of ways of doing that is: sum(i = 0, [(k-n)/s]) (-1)^i*C(k-si-1,n-1). Call this f(n,s,k). Note: [x] denotes floor of x, and C(a,b) is a choose b. Now: We essentially have five ten-sided dice, h...
Thu Feb 21, 2008 2:47 am UTC
Forum: Logic Puzzles
Topic: Matchsticks
Replies: 12
Views: 3474

### Re: Matchsticks

Spoiler:
Although, the initially posted solution seems like the only way to get 4 equilateral triangles with side length equal to the matchstick length.
Sat Feb 16, 2008 2:51 pm UTC
Forum: Logic Puzzles
Topic: Spaghetti breakfast [solutions]
Replies: 4
Views: 4630

### Re: Spaghetti breakfast [solutions]

Token wrote:
imatrendytotebag wrote:So average = n/(number of loops). Hence expected average = n/(expected number of loops) = n/f(n).

I'm not sure I like this step. In general, E(f(X)) != f(E(X)), so if you want to use that it will require proving.

Hm, yeah on second thought I'm probably wrong about that...
Sat Feb 16, 2008 6:46 am UTC
Forum: Logic Puzzles
Topic: Spaghetti breakfast [solutions]
Replies: 4
Views: 4630

### Re: Spaghetti breakfast [solutions]

Inductively... Consider n strands. Thor picks 1 end from the 2n ends. Now when he picks the end to tie it to, there is 1/(2n-1) chance he ties it to the same piece of spaghetti. Afterwards we have 1 loop and n-1 strands left. Otherwise we have (effectively) n-1 strands. So if f(n) is the expected nu...
Thu Feb 07, 2008 4:15 am UTC
Forum: Mathematics
Topic: quickly find nearest point
Replies: 4
Views: 1441

### Re: quickly find nearest point

Lets say x = (a+b)/2, and y = (a-b)/2. Then a = x + y and b = x - y. Similarly, letting z = (c+d)/2 and t = (c-d)/2, c = z + t, d = z - t. Then: (x+y)^2 + (x-y)^2 > (z+t)^2 + (z-t)^2 <=> x^2 + y^2 > z^2 + t^2 (x+y)*(x-y) < (z+t)*(z-t) <=> x^2 - y^2 < z^2 - t^2 In particular we have the inequality ch...
Sat Jan 26, 2008 6:24 pm UTC
Forum: Logic Puzzles
Topic: This week's cartalk.com puzzler
Replies: 12
Views: 3245

### Re: This week's cartalk.com puzzler

Say our number is ABCDEF. If F is 0-7, then The first condition implies CDEF is palindromic (C = F), the second condition implies BCDE(F+1) is palindromic (C = E and B=F+1), and the third condition implied BCDE is palindromic (B=E). By transitivity we get F = C = E =...
Thu Jan 17, 2008 2:44 am UTC
Forum: Mathematics
Topic: Mathematical Busking
Replies: 50
Views: 5085

### Re: Mathematical Busking

Ughhh man I am so so so tempted to steal this idea, its seriously brilliant. Good luck with it!