Search found 825 matches

by Torn Apart By Dingos
Mon Aug 28, 2006 9:31 pm UTC
Forum: Logic Puzzles
Topic: Marble Dropping [solution discussion]
Replies: 16
Views: 11865

Yes, that's right. :) Now, what's the best average we can get? Let n_1 be the first floor we drop the first marble from, n_2+n_3 be the second floor we drop it from, n_2+n_3+n_4 be the third floor, etc. Then the list of tries needed will be: [2, 3, ..., n_1, 1; 3, 4, ..., (n_2+1), 2; ...; (k+1), ......
by Torn Apart By Dingos
Mon Aug 28, 2006 5:03 pm UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

at the end of a complete cycle, x number of marbles will have been added, and then removed again from the jar, and so at the end of any cycle, the jar is empty No, moving marbles in and out of the jar is instantaneous. It must be, because if the number of marbles oscillated back and forth like that...
by Torn Apart By Dingos
Mon Aug 28, 2006 2:09 pm UTC
Forum: Logic Puzzles
Topic: Marble Dropping
Replies: 33
Views: 23148

I've got another solution, but unfortunately it wasn't better than my last one. It was easier to analyze, though (I used Python to calculate averages with my two first methods). It seems the only scheme you can use is to try to exclude as many floors as possible with the first marble, and use the se...
by Torn Apart By Dingos
Mon Aug 28, 2006 1:26 pm UTC
Forum: Logic Puzzles
Topic: Marble Dropping
Replies: 33
Views: 23148

Are we looking for the best average case or the best worst case? I guess it's okay to break both if that'll tell you what storey you're looking for? If not, you could only use the first marble and try floors 1,2,3,4,5... in order. If there were infinitely many floors, I'd probably do this: try the f...
by Torn Apart By Dingos
Mon Aug 28, 2006 9:09 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

Marbles: To say that something happens after an infinite number of steps makes no sense. There is no "after". Using some gimmick with fractions of a second doesn't help because the question should be restated "after a second that doesn't make any sense at all..." A similar opera...
by Torn Apart By Dingos
Sun Aug 27, 2006 5:25 pm UTC
Forum: Logic Puzzles
Topic: Three princesses
Replies: 446
Views: 204100

Re: Two Challenges, Three Princesses

It seemed that solving it depended on specifically knowing the relative ages of the princesses. You don't have to. You could use some other property, or even define one yourself. You could ask: "if i the lying princess is princess 1, the truthtelling one is princess 3, and the other one is pri...
by Torn Apart By Dingos
Sat Aug 26, 2006 6:03 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

ulnevets wrote:perhaps there is a physical limit involving the Planck time

That's pretty silly to consider. You couldn't have infinitely many marbles to start with, nor the energy to move them all.
by Torn Apart By Dingos
Thu Aug 24, 2006 1:24 pm UTC
Forum: Language/Linguistics
Topic: Why proper spelling is not important.
Replies: 27
Views: 9246

Seeimmoots the cbeeellrum ecennortus iacegilnnrsy oeeinoprrvwg oabcelsts: scefiipc caacehrtr paeirmnottus (aaclltuy aabehilptc laceghiiporxc). I am guessing you are saying something like, "The brain does not mind if there are repeated letters!" but I believe you are wrong. There are no ex...
by Torn Apart By Dingos
Thu Aug 24, 2006 6:44 am UTC
Forum: Language/Linguistics
Topic: Why proper spelling is not important.
Replies: 27
Views: 9246

Seeimmoots the cbeeellrum ecennortus iacegilnnrsy oeeinoprrvwg oabcelsts: scefiipc caacehrtr paeirmnottus (aaclltuy aabehilptc laceghiiporxc).
by Torn Apart By Dingos
Mon Aug 21, 2006 3:25 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

all of these paradoxes (except the first) do not exist in the real world. the real world cannot contain paradoxes, but imaginary ones can. Paradoxes are never paradoxes. There's a flaw in their logic, so your purpose is to find that flaw, not to be disintegrated in an implosion of contradiction. Th...
by Torn Apart By Dingos
Mon Aug 21, 2006 3:16 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

The sum of (1/2**n) = 1 when n ranges from 1 to infinity. Since the sum never reaches 1 in any finite amount of time (see Zeno's arrow), we never finish moving marbles in and out of the jar, so the rest of the question is irrelevant. Huh? The sum is indeed 1, so it will take a finite time (1!). I d...
by Torn Apart By Dingos
Sun Aug 20, 2006 6:02 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

That doesn't make sense to me. Whilst each step involves removing a set of marbles, it is then replaced with a larger set of marbles in the same step. Therefore we end up with an infinite number of marbles in the jar. Which marbles does it contain then? Each marble is identified by a number n. But ...
by Torn Apart By Dingos
Sun Aug 20, 2006 2:38 am UTC
Forum: Logic Puzzles
Topic: More fun with paradoxes
Replies: 48
Views: 22077

I'll give you my favorite paradox. Initially, we have an empty jar and a collection of marbles, numbered 1, 2, 3, ... (one for each natural number). We put the marbles numbered 1 to 10 into the jar. Then we wait for half a second, and then take the marbles out of the jar, and put in the marbles numb...
by Torn Apart By Dingos
Fri Aug 18, 2006 4:12 am UTC
Forum: General
Topic: How should I remember the string xkcd
Replies: 44
Views: 20576

davean wrote:No, and I believe that was 3 character.

Can't you let me win just this once? I never win. :'(

You were, btw, right: clicky! About 80% have been taken. Damn lazy domain hoggers.
by Torn Apart By Dingos
Thu Aug 17, 2006 10:46 am UTC
Forum: General
Topic: How should I remember the string xkcd
Replies: 44
Views: 20576

I remember reading that all the 4-character internet domain names have been registered. So I'm going to with that xkcd's a random 4 character string that happened to be available some time ago, and didn't have any real meaning before that.

Do I win?
by Torn Apart By Dingos
Thu Aug 17, 2006 9:12 am UTC
Forum: Site/Forum issues
Topic: Forum/server issues
Replies: 8
Views: 5629

Hm, for some reason the only thread I can't load is the Hilbert's Hotel thread. It's not some cache thing, because I tried loading it in Opera, IE7, Firefox and K-Meleon, and I even tried ssh-ing to another computer and loading it with lynx. It's not because it's big, because I can load larger threa...
by Torn Apart By Dingos
Wed Aug 16, 2006 6:53 pm UTC
Forum: Logic Puzzles
Topic: Hilbert's Hotel
Replies: 102
Views: 10500

without assuming the ability to complete a supertask . ... but any given guest will be asked to move a finite amount of time after the new one arrived at the hotel. If you're going to do that, I don't agree it's not a supertask. Any individual step will of course be done in a finite time, but the w...
by Torn Apart By Dingos
Wed Aug 16, 2006 4:27 pm UTC
Forum: Logic Puzzles
Topic: Hilbert's Hotel
Replies: 102
Views: 10500

without assuming the ability to complete a supertask . ... but any given guest will be asked to move a finite amount of time after the new one arrived at the hotel. If you're going to do that, I don't agree it's not a supertask. Any individual step will of course be done in a finite time, but the w...
by Torn Apart By Dingos
Mon Aug 14, 2006 3:56 am UTC
Forum: Logic Puzzles
Topic: Hilbert's Hotel
Replies: 102
Views: 10500

The essence of the seeming paradox is that "full" means "every room contains an occupant". Our intuition tells us this also means that no more rooms are available, but this is only necessarily true for a finite hotel -- in an infinite one, our common-sense notions don't always h...
by Torn Apart By Dingos
Sat Aug 12, 2006 4:09 am UTC
Forum: Logic Puzzles
Topic: Hilbert's Hotel
Replies: 102
Views: 10500

Shellsh0ck wrote:The only way you can make infinity into something other than infinity is to multiply it by zero.
Or you can raise 2 by infinity, resulting in a larger infinity (different from the one you started with).
by Torn Apart By Dingos
Fri Aug 11, 2006 8:23 pm UTC
Forum: Logic Puzzles
Topic: Hilbert's Hotel
Replies: 102
Views: 10500

The fun part is realizing that the hotel being "full" means the set of rooms and the set of guests have the same cardinality. No, it's the other way around. It's a necessary condition (the guests and the rooms must have the same cardinality if the hotel is full), not a sufficient one. The...
by Torn Apart By Dingos
Fri Aug 04, 2006 10:34 am UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418666

I can't explain quite what information the Guru gives them either. But I know the argument that he tells them something they already know doesn't work: Consider the case of two blue eyes. Then "everyone already knew" what the Guru told them. Yet, if you had blue eyes, and assume that you d...
by Torn Apart By Dingos
Thu Aug 03, 2006 11:40 am UTC
Forum: Logic Puzzles
Topic: Math paradox
Replies: 21
Views: 12602

Well, A=B=something is just another notation for {A=something, B=something}. What I'm doing in the examples is just substitution. I don't see any deeper reason for new solutions to pop up (why is {x|A(x)=B(x)} larger than {x|A(x)=s} union {x|B(x)=s}?). Specifically, why -1 in the first one? - if I i...
by Torn Apart By Dingos
Thu Aug 03, 2006 3:20 am UTC
Forum: Logic Puzzles
Topic: Math paradox
Replies: 21
Views: 12602

I would say that Example 2 also gives more solutions, not fewer. You're given the equation 1=1. Now what's x? It can be anything at all. More solutions, right. I'm a little tired. :) When you combine "expression A = something" with "expression B = something" to get "express...
by Torn Apart By Dingos
Thu Aug 03, 2006 3:00 am UTC
Forum: Logic Puzzles
Topic: Math paradox
Replies: 21
Views: 12602

I guess this paradox shows that the combination of two equivalent statements won't necessarily be equivalent to the first two. Example 1 (similar to the original poster's): x=1 is equivalent to 1/x=1. But x=1/x has an extra solution x=-1. Example 2: x=1 is equivalent to x=1. Combining these gives 1=...

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