## Search found 284 matches

Mon Oct 29, 2007 4:39 pm UTC
Forum: Logic Puzzles
Topic: 10,000 Doors
Replies: 26
Views: 3099

### Re: 10,000 Doors

All but 1, and revel in my 9999000 USD in all of those universes in which I survived?
Fri Oct 26, 2007 4:49 am UTC
Forum: Mathematics
Topic: cantor set = set of all what in base 3?
Replies: 3
Views: 1229

### Re: cantor set = set of all what in base 3?

IIRC n means "a finite number" here.

ETA: I do not recall correctly and did not do any checking of my recollection and it shows.
Fri Oct 26, 2007 12:42 am UTC
Forum: Mathematics
Topic: Hard combinatorics problem
Replies: 15
Views: 3043

### Re: Hard combinatorics problem

That's the reason I want to know. If the odds are better than 1/2, I'd make bets about it. "Hey, choose two values. I'll give you a dollar if no two cards of those two values are within 2 cards of one another, and you give me a dollar otherwise. I'll even let you shuffle!" I'd bet that yo...
Thu Oct 25, 2007 11:18 pm UTC
Forum: Logic Puzzles
Topic: 10 Word Puzzles
Replies: 17
Views: 3463

### Re: 10 Word Puzzles

6 is
Spoiler:
6 Mars
Thu Oct 25, 2007 4:32 pm UTC
Forum: Mathematics
Topic: Estimating a continuous distribution from a sample
Replies: 3
Views: 918

### Re: Estimating a continuous distribution from a sample

Are you working on a specific problem? If so can we see it?
Thu Oct 25, 2007 5:57 am UTC
Forum: Mathematics
Topic: Hard combinatorics problem
Replies: 15
Views: 3043

### Re: Hard combinatorics problem

No, he is choosing 4 slots for four Aces with replacement (assume that aces are always inserted to one side of a slot. . .they don't use it up, and the 4! reordering of aces takes care of the problem of new aces creating new slots (we can assume they don't). . .thus, the number of slots always rema...
Tue Oct 23, 2007 9:12 pm UTC
Forum: Mathematics
Topic: continuous distributions with point masses, centers of mass
Replies: 4
Views: 1238

### Re: continuous distributions with point masses, centers of mass

You can't make point particles with a density function. If you give a finite density to a single point, that has zero mass. But yes, replacing a large object with a point particle at its center doesn't change the center of the whole system. Dirac delta function. What you actually want to do is put ...
Mon Oct 22, 2007 5:10 pm UTC
Forum: Mathematics
Topic: Probability
Replies: 22
Views: 1998

### Re: Probability

I think I'm starting to wrap my head around this. To clarify, the Bayesian approach states that probability is not so much a "vague" element of physics, but merely represents the variables we do not know -- and thus, if we knew every variable in the universe, there would be no chance or p...
Mon Oct 22, 2007 6:30 am UTC
Forum: Mathematics
Topic: Probability
Replies: 22
Views: 1998

### Re: Probability

So I guess, it's about taking into account everything we know, and actually doing a real test, and seeing that the results support each other. Not quite. It's about taking into account everything we know, then actually doing a real test. Now let's say we wanted to do another test. Take into account...
Mon Oct 22, 2007 1:27 am UTC
Forum: Mathematics
Topic: Probability
Replies: 22
Views: 1998

### Re: Probability

A shorter summary of Jaynes: Things do not contain a magical property called "probability". A "fair coin" only has probability 1/2 of landing on heads if you have no reason to believe it will land on heads or tails. Probability is instead a number we use to represent our state of...
Sun Oct 21, 2007 8:35 pm UTC
Forum: Mathematics
Topic: Probability
Replies: 22
Views: 1998

### Re: Probability

I second the motion to read E. T. Jaynes. But if you want a summary of the position, here you go, I wrote one a few weeks ago: link
Fri Oct 19, 2007 9:48 pm UTC
Forum: Mathematics
Topic: problem in discrete math
Replies: 4
Views: 1158

### Re: problem in discrete math

A good approximation is just looking at those values of n such that n=2^k. The result should fall out from there.
Thu Oct 18, 2007 4:57 am UTC
Forum: Mathematics
Topic: Hard combinatorics problem
Replies: 15
Views: 3043

### Re: Hard combinatorics problem

Yes, when I said "essentially equivalently" I meant that one answer would give the other, not that they give the same answer. I'm guessing here that 0.486. . . was the probability of an ace next to a jack and 0.581. . . was no aces next to jacks? Or is that backwards? Yep, that's right. J...
Thu Oct 18, 2007 1:41 am UTC
Forum: Mathematics
Topic: Hard combinatorics problem
Replies: 15
Views: 3043

### Re: Hard combinatorics problem

skeptical scientist wrote:Without doing any math or trying to figure out what you're doing, I notice that .486ish is 1-.5137...

Did you perhaps calculate the probability of something not happening instead of it happening?

Haha, clearly. The program was counting times a 0 was next to a 1, not times it wasn't. Good catch.
Thu Oct 18, 2007 12:43 am UTC
Forum: Mathematics
Topic: The hardest part of my math test..
Replies: 37
Views: 6465

### Re: The hardest part of my math test..

Multiple choice is nice, so long as, like my CS250 proffessor, you don't add "(e) Not one of the answers." to every question. The UKSMC papers I used to do occasionally had this option for a question (specifically, "E: More information needed.") It actually increased the chance ...
Thu Oct 18, 2007 12:29 am UTC
Forum: Mathematics
Topic: Hard combinatorics problem
Replies: 15
Views: 3043

### Re: Hard combinatorics problem

Name two card values (not suits) in a standard deck of 52 cards. What are the odds that two cards of those values (in any suit) are adjacent (in either order) in the deck at least once? (or, essentially equivalently, how many deck orderings do not contain that pair of values adjacent to one another...
Wed Oct 17, 2007 10:01 pm UTC
Forum: Logic Puzzles
Topic: Sphere intersection
Replies: 6
Views: 2372

### Re: Sphere intersection

Points, yes. But D doesn't determine a chord. You'd still have to do something like "and then pick a direction normal to 'towards the midpoint' at random, and make that your chord". Okay, so the question could be "Suppose you are in the middle of two fragile spheres, one twice the rad...
Wed Oct 17, 2007 9:34 pm UTC
Forum: Logic Puzzles
Topic: Sphere intersection
Replies: 6
Views: 2372

### Re: Sphere intersection

If you know the parameter D = "distance from the midpoint", that's enough to determine whether the line intersects the inner sphere, but it seems very hard to come up with a physical experiment where D is uniform [0,R].
Wed Oct 17, 2007 8:55 pm UTC
Forum: Logic Puzzles
Topic: Sphere intersection
Replies: 6
Views: 2372

### Sphere intersection

We've just seen Bertrand's Paradox come up in another thread. Here's an extension: Pick a random line that goes through a sphere. With what probability does the line go through another sphere with the same midpoint but with half the radius? How many sensical interpretations are there? Which would yo...
Thu Sep 27, 2007 5:22 pm UTC
Forum: Mathematics
Topic: Challenge Math
Replies: 9
Views: 1747

### Re: Challenge Math

For 1<=k<=n, after turn k the kth coin will be tails so we're not done. For n<=k<2n, the nth coin will be tails so we're not done. After turn 2n, each type of flip will have occurred twice, so no matter which flips a coin is involved in, it will have been flipped an even number of times and will end...
Sat Sep 22, 2007 9:11 pm UTC
Forum: Mathematics
Topic: Word Numbers Puzzle
Replies: 33
Views: 4446
I think Sriad was replying to ffguy, not me. Mine does find the sum as well... in fact, if you don't care about the sum, it can find the 51 billionth letter in less than 20 seconds. My mistake. So what was the letter you came up with Sriad? Was it indeed one of these letters? e, d, n, o, r, t, x, o...
Wed Sep 19, 2007 5:27 am UTC
Forum: Logic Puzzles
Topic: Be Fruitful and Multiply [solution thread]
Replies: 10
Views: 3758
skeptical scientist wrote:Was it either of the ones we came up with? Can you give a quick sketch?

I've seen the same proof Cauchy gave before, I believe in a lecture on Markov chains.
Sun Sep 16, 2007 8:13 pm UTC
Forum: Logic Puzzles
Topic: Choose signs to make a complex series converge
Replies: 61
Views: 9091
Someone needs to post a solution or hint, because otherwise I will draw more circles in my idle time.
Sun Sep 09, 2007 7:39 pm UTC
Forum: Language/Linguistics
Topic: George Orwell, "Politics and the English Language."
Replies: 4
Views: 4352
Strunk & White is politics and the English language.
Tue Sep 04, 2007 11:51 pm UTC
Forum: Logic Puzzles
Topic: Meta-puzzle: Who is the prisoner?
Replies: 10
Views: 3516
#1:
Delicious waffles?
Tue Sep 04, 2007 11:19 pm UTC
Forum: Logic Puzzles
Topic: Meta-puzzle: Who is the prisoner?
Replies: 10
Views: 3516
You are Number 6.
Mon Aug 27, 2007 11:38 pm UTC
Forum: Logic Puzzles
Topic: Choose signs to make a complex series converge
Replies: 61
Views: 9091
Lemma proof: Edit: Misunderstood lemma to be proven. This does not work. But maybe you can manhandle it into something nice that does. Lemma: There is a number M so that given any n and any finite sequence c_1...c_n of length n, with |c_i|<1 for all i, there is a choice of signs s_1...s_n in {1, -1}...
Wed Aug 22, 2007 7:41 pm UTC
Forum: Gaming
Replies: 154
Views: 62445
I'd also suggest Through the Desert (Durch die WÃ¼ste) at Ludagora. It hits the same cognitive sweet spots that Go does, and is multiplayer.
Thu Aug 16, 2007 6:04 am UTC
Forum: Mathematics
Topic: WLOG
Replies: 7
Views: 3090
Usually whenever there are one or more things that have symmetry and you are choosing one specific thing but it doesn't matter which. For example, I flip a coin twice. What are the odds I get the same result twice? WLOG, the first flip is heads. The second flip has a 50% chance of being heads, so th...
Sun Aug 05, 2007 10:27 pm UTC
Forum: Logic Puzzles
Topic: Riddles from a friend
Replies: 31
Views: 7033
Sure, there may be many "working" answers, but nothing in the riddle points to them as being the correct answer. Asking questions about the riddles may make them easier, but the real key to them is that there is always something in the riddle that gives it away. For example, question E: E...
Fri Jul 06, 2007 5:19 pm UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13470
So what is the point of this topic? It seems like you just asked some arbitrary question that you knew wasn't really possible and doesn't make much logical sense, yet you asked it anyway. Well, it got a hell of a lot of response, so I think I justified the creation of this thread simply with that. ...
Mon Jul 02, 2007 3:33 pm UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233
H-Bar wrote:From the rest of the comments I assume the prisoners can do something with the names, but this can't be it.

The room is exactly the same for each prisoner. If they move names around, first they are beaten, then the guard puts the names back where they should be.
Sun Jul 01, 2007 11:59 pm UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233
V wrote:Theese guys are named
Curtin and Warshauer
. The paper is called
The locker puzzle
.

Good find!
Sun Jul 01, 2007 6:38 pm UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233
Cauchy wrote:How expected is it for newcomers to introduce themselves? I didn't, and I really don't like intro threads on principle, but I've been posting here for three months. Am I sufficiently not a newcomer to escape my otherwise unavoidable fate?

I agree wholesale.
Sun Jul 01, 2007 4:46 pm UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233
I have a strategy that works just over 31% of the time, but I've never seen a proof that it's optimal. I'm pretty sure it's the intended solution, though. The boxes are distinguishable, and the prisoners know this beforehand and know what the 100 boxes look like. For ease of argument, the boxes are...
Sun Jul 01, 2007 10:02 am UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233
Yep. The guard closes all the boxes after a prisoner is done with his <= 50 tries. Assume the room is memoryless, prisoners can't talk with subsequent prisoners, etc. etc.
Sun Jul 01, 2007 9:44 am UTC
Forum: Logic Puzzles
Topic: 100 prisoners need to find their names
Replies: 23
Views: 10233

### 100 prisoners need to find their names

Once again 100 prisoners are locked up with a quirky chance of being released. This time the guard tells them he will bring them one at a time into a room with 100 boxes. Each box contains one of their names (they all have unique names and each of their names is in some box). Each prisoner may look ...
Mon Jun 25, 2007 4:56 am UTC
Forum: Mathematics
Topic: The mathematician with the most theorems
Replies: 9
Views: 3328
There will be no civil wars, do not worry. Anyone who thinks the answer is not Euler cannot be civil.
Fri May 18, 2007 2:07 pm UTC
Forum: Coding
Topic: Does anyone here compete on Topcoder?
Replies: 30
Views: 14936
2. People get ridiculously defensive of their favorite time-wasting hobby and keep a topic alive a lot longer than it strictly deserves to be as a side-effect. Last person to post in this thread wins. But yeah, essentially it is nothing but a time-wasting hobby that some people find enjoyable and o...
Thu May 17, 2007 4:36 pm UTC
Forum: Coding
Topic: Does anyone here compete on Topcoder?
Replies: 30
Views: 14936
There are all kinds of interesting, but academic-looking problems that satisfy a real-world need. There is code in virtually any application that (outside of the context of the application it was written for) will seem 'utterly useless'. Naturally, such a contest would contain a lot of 'filler' pro...