## Search found 82 matches

- Wed Oct 18, 2017 2:11 pm UTC
- Forum: Logic Puzzles
- Topic: Could there still be new hat puzzles?
- Replies:
**12** - Views:
**9946**

### Re: Could there still be new hat puzzles?

Well, I was right - there is a much more elegant maximal strategy. You don't even need to divide it up into cases to use the strategy (though checking it will divide into cases)! Check the players that are first, second, and fourth from your left. Guess whichever color hat is worn by an even number...

- Thu Oct 12, 2017 9:55 pm UTC
- Forum: Logic Puzzles
- Topic: Could there still be new hat puzzles?
- Replies:
**12** - Views:
**9946**

### Re: Could there still be new hat puzzles?

Well, I was right - there is a much more elegant maximal strategy. You don't even need to divide it up into cases to use the strategy (though checking it will divide into cases)! Check the players that are first, second, and fourth from your left. Guess whichever color hat is worn by an even number ...

- Sat Oct 07, 2017 4:47 pm UTC
- Forum: Forum Games
- Topic: This is not a game!
- Replies:
**18** - Views:
**1985**

### Re: This is not a game!

Wait, since this is not a game, does this mean I can jump straight to Mornington Crescent?

- Sat Oct 07, 2017 4:41 pm UTC
- Forum: Logic Puzzles
- Topic: Could there still be new hat puzzles?
- Replies:
**12** - Views:
**9946**

### Re: Could there still be new hat puzzles?

Proof of a theoretical maximum, assuming a deterministic strategy: EDIT: Actually, I don't even think we need to assume a deterministic strategy. I'll edit my argument in. There are 128 configurations of hats. Each player, in any given deterministic strategy, will be right in 64 cases and wrong in t...

- Fri Jul 21, 2017 1:21 pm UTC
- Forum: Logic Puzzles
- Topic: Isosceles triangles and circles : puzzle connection
- Replies:
**15** - Views:
**6676**

### Re: Isosceles triangles and circles : puzzle connection

The right to progress is to ask for clarity before trying to solve the puzzle. I assumed that people finding quickly trivial solutions will ask themselves why before posting. I was wrong. It's an interesting philosophical question: who is responsible for making sure the solver completely understand...

- Fri Jul 14, 2017 12:00 am UTC
- Forum: Logic Puzzles
- Topic: Connection game : Fertility
- Replies:
**6** - Views:
**4588**

### Re: Connection game : Fertility

I've had another realization. Take a look at this configuration of pieces (M is male, F is female, O is offspring, and x is an opponent's piece of some kind): M x x x O O x F O x O F x O O x M x x If you are forced to make two paths, one of the offspring has to be excluded. However, if you are allow...

- Thu Jul 13, 2017 9:29 pm UTC
- Forum: Logic Puzzles
- Topic: Connection game : Fertility
- Replies:
**6** - Views:
**4588**

### Re: Connection game : Fertility

So to restate the rules of the game: ⋅ The game is played between two players (Red and Blue) on a Hex board of a certain size. ⋅ Each player received a set of player-colored pieces: 3 male, 3 female, and sufficient offspring to fill the board. ⋅ Starting with Blue, play...

- Tue Jun 20, 2017 2:19 pm UTC
- Forum: Logic Puzzles
- Topic: Pirate Game with New Priorities
- Replies:
**6** - Views:
**5357**

### Re: Pirate Game with New Priorities

I had somewhat intended K to be killing other pirates , but you did cover that. I agree with all the above, with the exception of: For LKC: Now the pirates still care about killing other pirates more than about getting coins, but not at the cost of their own lives. When it gets down to D and E, D w...

- Tue Jun 20, 2017 1:38 pm UTC
- Forum: Logic Puzzles
- Topic: Pirate Game with New Priorities
- Replies:
**6** - Views:
**5357**

### Re: Pirate Game with New Priorities

I was going to claim that we can rule out any case where C comes before L, because L needs to happen in order for C to go above 0, but that's not quite right - there is one change: now the pirates no longer care about living if they're not going to get any gold, at least not immediately. We can stil...

- Sat Jun 17, 2017 7:06 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

Which brings me to my second point, which I now realize was not given enough emphasis/worded in a confusing manner: the function h(x) is not the end of the story. It merely tells us what term of the original sequence (X's included) should be used in the new sequence (X's excluded). Aww, I got that ...

- Fri Jun 16, 2017 1:38 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

From this point, since the numbers we want to skip are those two less than odd composites, for any x, let y=h(x+2)-2, and then calculate the value for that y. x = 9 y = h(9 + 2) - 2 y = h( 11 ) - 2 y = 12 - 2 y = 10 9,10 However, the correct mapping is 9,2. First of all, for what I'm trying to acco...

- Fri Jun 16, 2017 3:59 am UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

I'm not entirely sure where you're going with this. Could you give an example of where term N and term -N are unequal? 'N' and '-N' will always give the same value, but it is a very reasonable mistake to think the opposite. In order for a number to be the output, it must be a sibling. Someone could...

- Thu Jun 15, 2017 1:21 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

Thank you very much for the explanation. I have some more questions. Of course, this function may do weird things with values of x less than 2, but we are not considering the function for any values of x less than 3 anyway. That may be a problem. Something I realized last night is that using 0 and ...

- Wed Jun 14, 2017 9:27 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

Second point first: yes, that is a conjecture, and it is generally accepted as true, but to the best of my knowledge it has not yet actually been proved. If that conjecture happens to be false, the algorithm needs to be modified to take that into account. First point second: Admittedly I misspoke in...

- Wed Jun 14, 2017 6:10 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**8630**

### Re: Guess the Pattern

If we are able to calculate, as a function f, the number of primes less than or equal to a given number x, then we could iterate x 0 = x, x i+1 = x+f(x i ) until it converges, and use it to calculate our term N (or something similar to this method). After all, the only way an odd nu...

- Sat May 27, 2017 3:33 pm UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

Yeah, it was. Fixed it.

- Fri May 26, 2017 2:58 am UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

I'm not (yet) convinced your argument works, though - I'm stuck here: From these equations, and the fact that all probabilities are negative, we can deduce (K) p1XX>1/7, (L) pX2X>1/7, and (M) pXX3>1/7 Can you explain how you make this assumption and deduction? Sure, no probl...

- Fri May 26, 2017 12:12 am UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

Yeah, that's my solution. I realized that since the Picker could not preserve two m-tuples of points that are mutually-exclusive, every pair of m-tuples in the set of m-tuples the Picker preserves have to share at least one point. My intuition was that in order to spread out the m-tuples as much as ...

- Thu May 25, 2017 11:57 am UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

The Guesser begins with every subset of size m of the set of numbers as a possibility. If there are two such subsets {a 1 , a 2 , ..., a m } and {b 1 , b 2 , ..., b m } of which their elements are mutually exclusive, the guesser may eliminate one set or the other from the list of possibilities, wit...

- Thu May 25, 2017 4:08 am UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

Still reading through the second half of your solution, but had a question on this: ...for it is always possible for the Guesser to eliminate one of two mutually-exclusive sets... I don't see why this needs to be true (and if true it seems like it solves the whole problem on its own). Did you mean ...

- Wed May 24, 2017 9:33 pm UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

I think I've got it: Let the players be called the Picker, who chooses the numbers, and the Guesser, who makes the guesses. Let the Picker's strategy be as follows: Select an arbitrary finite projective plane (of order m-1) over m^2-m+1 points (assume N is sufficiently large for the ...

- Tue Apr 25, 2017 12:03 am UTC
- Forum: Logic Puzzles
- Topic: Two more secrets
- Replies:
**17** - Views:
**8157**

### Re: Two more secrets

If by a "winning strategy" you mean one that is guaranteed to win: For N>=3, which are the only values of N for which this game makes sense anyway, no. Your response is as follows: letting your two numbers be x and y, you can select a single "fake" number z, distinct from these t...

- Mon Apr 24, 2017 1:56 am UTC
- Forum: Logic Puzzles
- Topic: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles
- Replies:
**8** - Views:
**4805**

### Re: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles

A small additional correction: In your updated logic for the last step, you forgot to replace "x1 >= 4" with the newly computed "x1 >= 5", so you were off by one – the number in the problem needs to be 15, and the answers are (7, 1) and (9, 2). You're right, don'...

- Sun Apr 23, 2017 10:52 pm UTC
- Forum: Logic Puzzles
- Topic: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles
- Replies:
**8** - Views:
**4805**

### Re: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles

About why the puzzle is broken: I believe the infinite sequence currently eliminates EVERY possible choice of values, although it's very complex to see why. Figuring that out is a pretty interesting puzzle in its own right. I wonder what would be a good way to make that into an explicit puzzle ...

- Sun Apr 23, 2017 1:17 pm UTC
- Forum: Logic Puzzles
- Topic: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles
- Replies:
**8** - Views:
**4805**

### Re: A very fiendish one of those "figure out the answer based on logicians not knowing the answer" puzzles

(I just wrote this. I sure hope I did the logic right.) Jane, Emily, and Mike were perfect logicians. One day, Jane said, "I'm thinking of four nonnegative integers, x1, y1, x2, and y2, that obey the following conditions: |x1 - x2| >= 1 |x1 - x2| >= min(y1, y2) |x1 - x2| <= 1 + min(y1, y2) |y1...

- Wed Apr 05, 2017 6:37 pm UTC
- Forum: Logic Puzzles
- Topic: Two secrets
- Replies:
**20** - Views:
**9877**

### 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:
**9877**

### 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:
**9877**

### 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:
**12375**

### 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:
**9877**

### 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:
**3873**

### 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:
**4344**

### 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:
**17** - Views:
**11305**

### 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:
**116881**

### 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:
**116881**

### 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:
**116881**

### 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:
**116881**

### 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:
**116881**

### 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:
**5133**

### 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:
**5133**

### 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...