## Search found 57 matches

- Wed Apr 05, 2017 6:37 pm UTC
- Forum: Logic Puzzles
- Topic: Two secrets
- Replies:
**20** - Views:
**1700**

### Re: Two secrets

I just realized we can improve sfwc's method to only require O(log(N)^3) questions: If any of g, h, i, and j are the same, we can get rid of a duplicate, and reduce the lengths of the sequences in T accordingly, with no change. For example, if i and j are the same, we can get rid of j, remove the la...

- Sun Apr 02, 2017 4:01 pm UTC
- Forum: Logic Puzzles
- Topic: Two secrets
- Replies:
**20** - Views:
**1700**

### Re: Two secrets

In truth, N = 5 should require only 3 questions. It's true that adversarially the secret-holder will always answer "no" to a 2-element question if possible (otherwise, guessing those 2 elements will guarantee at least one is in the set), but if you strategically ask about, let's say, {1, ...

- Fri Mar 31, 2017 6:50 pm UTC
- Forum: Logic Puzzles
- Topic: Two secrets
- Replies:
**20** - Views:
**1700**

### Re: Two secrets

So we just have to show that for any distinct a, b, c and d we can find g, h, i, j and T with a and b but neither c nor d in S(g,h,i,j,T). Let g be the position of any digit where a and c differ, h the position of a digit where a and d differ, i the position of a digit where b and c differ ...

- Fri Mar 31, 2017 4:58 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs
- Replies:
**12** - Views:
**6796**

### Re: Infinite Balls and Jugs

Suppose I have infinitely many balls, each labelled with a different specification for a Turing machine(of which there are countably many) so that I have all the Turing Machines ordered in some easily specifiable way. I set the value N to 1 and turn my attention toward the first TM. At 10 minutes, ...

- Wed Mar 29, 2017 3:27 am UTC
- Forum: Logic Puzzles
- Topic: Two secrets
- Replies:
**20** - Views:
**1700**

### Re: Two secrets

For N = 5, asking about 0, 1, 4, or 5-element subsets is fruitless (since the secret-holder can always answer "no", "no", "yes", and "yes", respectively), and asking about a 3-element subset is the same as asking about its complement (since whatever the answe...

- Sun Mar 26, 2017 10:58 pm UTC
- Forum: Logic Puzzles
- Topic: Pirate Game - A Variation
- Replies:
**1** - Views:
**452**

### Pirate Game - A Variation

You all know the classic Pirate Game - five pirates find a treasure of gold and have to divide it among themselves. The most senior/fiercest/whatever pirate proposes a division, and if it does not get 50% of the vote, that pirate is killed and the next pirate makes a proposal. It's an old one, it's ...

- Sun Mar 26, 2017 1:44 pm UTC
- Forum: Logic Puzzles
- Topic: Situational Logic Puzzle
- Replies:
**5** - Views:
**414**

### Re: Situational Logic Puzzle

There are some parts of this puzzle that are unclear. I mean, why does everyone get $1M right off the bat? In the source material for this game it made sense, but if players actually die when they are in the majority, it doesn't make sense any longer. Plus, the "solution" from the source m...

- Thu Mar 09, 2017 10:14 pm UTC
- Forum: Logic Puzzles
- Topic: MisterGC's PUZZLES
- Replies:
**16** - Views:
**1853**

### Re: MisterGC's PUZZLES

As enlightening as this discussion is, it can actually be deduced from the clues themselves who the second male is (and, in fact, if you assume a binary gender system, the gender of every person can be deduced): By clue 5, there must be exactly two men due to grammar. By clue 3, the men host discuss...

- Sat Dec 24, 2016 3:54 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

In which case, the whole paradox boils down to saying "I want you to actually finish counting an infinite number of things (the discarded balls) without getting to an infinite number (the lowest-numbered ball remaining). You know, I did say: The first halves and second halves never "finis...

- Fri Dec 23, 2016 1:42 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

There are still several other posts that require your attention, kryptonaut. Just saying that before I begin. I mean, I don't want it to seem like you're avoiding them. The key part is ' if you could complete the infinity of tasks '. Each task TCn says 'wait for m steps, move ball n, wait for anothe...

- Wed Dec 21, 2016 4:11 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Your problem is your continued insistence that somehow balls like ω and ω+1 and 2ω just magically show up. All the balls we started with had natural numbers on them. So which natural number was originally on the now-lowest ball in the jug, which you claim is now numbered at least ω? When did it acq...

- Sat Dec 17, 2016 1:32 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Surely midnight can't arrive, because the person moving these balls around has to move faster and faster to do so and will thus experience time more and more slowly. Also, if the distance between "in the jug" and "out of the jug" is a piffling 1cm, by the time you've only got 1/...

- Fri Dec 16, 2016 7:41 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

I've been thinking some more about this (don't groan :) ), particularly in light of mward's post . I imagined an infinitely long train with numbered carriages, passing through a station. At any finite time it's possible to say which carriage is passing through - but after an infinite number of carr...

- Fri Dec 16, 2016 3:35 pm UTC
- Forum: Logic Puzzles
- Topic: Word Puzzle.
- Replies:
**6** - Views:
**1318**

### Re: Word Puzzle.

Regarding SOWPODS, I picked up the words from here to use. We only need to consider word pairs - i.e. pairs of words such that each is the other reversed. Additionally, we only need to consider word pairs where the three letters used are each unique - so eel/lee, for example, would be eliminated. Fr...

- Tue Dec 13, 2016 8:00 pm UTC
- Forum: Logic Puzzles
- Topic: Word Puzzle.
- Replies:
**6** - Views:
**1318**

### Re: Word Puzzle.

Yeah, with the word set jaap provided in the spoiler, it's not possible. Consider the word in the middle row. This word consists of the middle letter of the words in each of the three columns. Therefore, this word must be made entirely up of letters in the middle of some word. The only seven letters...

- Tue Dec 13, 2016 2:45 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

What happens when x is infinite? First, x cannot be part of Bj for any finite j, since since each finite Bj only contains finite values. So now, we need to do the same here... in order for L_inf to be non-empty there needs to be some specific I_j which is non-empty. What stops me from arguing the s...

- Sun Dec 11, 2016 7:43 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

You claim this is not one of those times. Are you making that claim just because the consequences of it being the natural numbers go against your finite-set-based intuition? Or is there some more concrete reason? I claim there are numbers that take an infinite number of steps to count to, for the v...

- Sat Dec 10, 2016 4:02 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Demki wrote:If they don't say that explicitly, they are using non-standard notation without informing about it, and are communicating badly.

And we all know what happens to people who communicate badly.

- Fri Dec 09, 2016 4:31 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

The puzzle starts " Suppose I have infinitely many balls, numbered 1,2,.. and so on. " It says nothing about finite numbers, or natural numbers. Just "infinitely many balls". If you actually count them all , it's no surprise you get an infinite number. If you try to model it usi...

- Fri Dec 09, 2016 2:44 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

In the original problem and the original problem only, what mechanism is used to create balls with infinite labels? By starting an infinite task and actually finishing it . We set out to count to infinity and we got there . We didn't just tend towards it , we really did it . The whole thing. Done. ...

- Fri Dec 09, 2016 1:53 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Then let's try a different tactic. We are not merely dealing with a generic "fully instantiated infinite set of numbers" - we are dealing with a particular set: the natural numbers. So let's talk about those. How do you define the natural numbers? I ask "why are we dealing with an in...

- Thu Dec 08, 2016 3:08 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

We have differing opinions on whether a fully instantiated infinite set of numbers includes infinite numbers or not. So whatever I answer here will only lead to us going round in circles. Then let's try a different tactic. We are not merely dealing with a generic "fully instantiated infinite s...

- Tue Dec 06, 2016 1:10 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

If L were merely infinite, then your argument might have some merit. However, L is not merely infinite - it contains ALL the natural numbers. There isn't any mapping going on here. ALL the natural numbers from 1 to where? The only way to compare them is to set up a 1:1 mapping. "ALL the natura...

- Mon Dec 05, 2016 2:43 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Now consider the three-partition L-C-R scenario. At the end of the supertask, all the natural numbers are in L. It doesn't matter how it gets there, it just matters that it gets there. Now, we'll call set U the union of C and R. Set U contains all the natural numbers that are not in L. Do you agree...

- Wed Nov 30, 2016 7:22 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

But you can put the 10% of the naturals you took away in a bijection with the entire set of naturals, in their usual order. (For example, if you took out 1, 11, 21, etc. you could use 1 -> 1, 11 -> 2, 21 -> 3, etc.) 10% of the naturals is the exact same size as the naturals. And when you try to tak...

- Wed Nov 30, 2016 2:05 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

Can you prove that it's even possible to divide N this way? And can you prove that the puzzle does force this division? It's not possible to take set N and pick a specific number partway up the set. But it's possible to construct two sets simultaneously, using every member from N , but keeping the ...

- Tue Nov 29, 2016 7:28 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

And it's possible that I've missed your explanation on where the infinite numbered balls came from since they did not exist at the start. Would you mind pointing it out to me? They arise because the set N is divided in the way I just described, at a point relative to the size of N . The numbers in ...

- Tue Nov 29, 2016 5:06 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

The trouble is, what we're dealing with in the original problem is the natural numbers in their usual ascending order. In order for your "infinite numbers" to exist, there needs to be an infinite amount of numbers followed by something. This doesn't happen with the natural numbers in thei...

- Tue Nov 29, 2016 4:06 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**52911**

### Re: Infinite Balls and Jugs [solution]

The only way for that tower to have nonzero size is if each piece decreases in size(say the size of the section halves with each step), so wherever you point, it is part of some finite section corresponding to a natural number, if you point from above straight down at the top, there is no number yo...

- Mon Nov 21, 2016 1:34 pm UTC
- Forum: Logic Puzzles
- Topic: Hidden Cards
- Replies:
**5** - Views:
**1349**

### Re: Hidden Cards

I see your 46 and raise you 47 with the following strategy: Rather than having a random uncertain logician guess the number on their blue card, the logician with the lowest remaining blue card should guess the number on their red card. This still makes it public knowledge what B(i 0 ) is, an...

- Fri Mar 11, 2016 5:46 am UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**2496**

### Re: Three Water Tanks

Two points towards curiosityspoon's solution: Minor point: All pumping activities can be finished in the 5 minutes it takes you to move from one tank to the other. So there's an epsilon for you - it takes 5 minutes to move between tanks. Major point, in response to your first paragraph: Let's take y...

- Thu Mar 10, 2016 10:40 pm UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**2496**

### Re: Three Water Tanks

Can there wind up being a non-integer amount of water in any given tank? For example, if the capacity was 40 liters, and first you request 15 liters from tank A, so the division is 25:40:40, and then an hour later you request 40 liters from tank A. Would it fill up so that the ratio is 40:32.5:32.5?...

- Fri Mar 04, 2016 2:50 pm UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**2412**

### Re: Optimize tiling for a 50x50 grid

Nice job filling in the whole grid. If I'm doing the math right, that's 1934 points. On the other hand, there's no penalty for leaving squares unfilled. Here's my solution: it leaves 2 squares unfilled and scores 1942 points. I used 8 5x5 tiles and discarded a 5x4 and a 5x3. http://i.imgur.com/DhpI0...

- Sun Jul 08, 2007 3:42 pm UTC
- Forum: Forum Games
- Topic: Text-based counterstrike
- Replies:
**41** - Views:
**10771**

>Y You are in the Library. You don't know who you are, but you must determine your character. There are closed doors to corridors to the North and to the West. You see Miss Scarlet out the window sneaking about. >OPEN NORTH DOOR You open the door. You spy Prof. Plum going into the Billiard Room thro...

- Thu Jul 05, 2007 3:25 pm UTC
- Forum: Forum Games
- Topic: Count to one thousand
- Replies:
**361** - Views:
**29200**

- Wed Jul 04, 2007 2:54 pm UTC
- Forum: Logic Puzzles
- Topic: Traveler's Dilemma
- Replies:
**833** - Views:
**61562**

- Mon Jul 02, 2007 11:26 pm UTC
- Forum: Forum Games
- Topic: Count to one thousand
- Replies:
**361** - Views:
**29200**

- Fri Jun 29, 2007 12:36 pm UTC
- Forum: Forum Games
- Topic: Fibs
- Replies:
**32** - Views:
**4044**

That one turns out longer than the one that I wrote. However, I don't think it counts. There's a change in count - letters instead of syllables. If someone could write a longer one using syllables instead of letters like him, please do so, so that I can say that you have completely broken the record...

- Thu Jun 28, 2007 12:45 pm UTC
- Forum: Forum Games
- Topic: Changing words
- Replies:
**296** - Views:
**24062**

- Thu Jun 28, 2007 12:45 pm UTC
- Forum: Forum Games
- Topic: you're fired!!!!
- Replies:
**45** - Views:
**6079**