## Search found 825 matches

- 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), ......

- 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...

- 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...

- 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...

- Mon Aug 28, 2006 9:09 am UTC
- Forum: Logic Puzzles
- Topic: More fun with paradoxes
- Replies:
**48** - Views:
**22077**

- 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...

- Sat Aug 26, 2006 6:03 am UTC
- Forum: Logic Puzzles
- Topic: More fun with paradoxes
- Replies:
**48** - Views:
**22077**

- Thu Aug 24, 2006 1:24 pm UTC
- Forum: Language/Linguistics
- Topic: Why proper spelling is not important.
- Replies:
**27** - Views:
**9246**

- Thu Aug 24, 2006 6:44 am UTC
- Forum: Language/Linguistics
- Topic: Why proper spelling is not important.
- Replies:
**27** - Views:
**9246**

- 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...

- 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...

- 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 ...

- 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...

- 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.

- Thu Aug 17, 2006 10:46 am UTC
- Forum: General
- Topic: How should I remember the string xkcd
- Replies:
**44** - Views:
**20576**

- 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...

- 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...

- Wed Aug 16, 2006 4:27 pm UTC
- Forum: Logic Puzzles
- Topic: Hilbert's Hotel
- Replies:
**102** - Views:
**10500**

- Mon Aug 14, 2006 3:56 am UTC
- Forum: Logic Puzzles
- Topic: Hilbert's Hotel
- Replies:
**102** - Views:
**10500**

- Sat Aug 12, 2006 4:09 am UTC
- Forum: Logic Puzzles
- Topic: Hilbert's Hotel
- Replies:
**102** - Views:
**10500**

- Fri Aug 11, 2006 8:23 pm UTC
- Forum: Logic Puzzles
- Topic: Hilbert's Hotel
- Replies:
**102** - Views:
**10500**

- 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**

- 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...

- Thu Aug 03, 2006 3:20 am UTC
- Forum: Logic Puzzles
- Topic: Math paradox
- Replies:
**21** - Views:
**12602**

- 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=...