Search found 75 matches

by Poker
Tue Jun 20, 2017 2:19 pm UTC
Forum: Logic Puzzles
Topic: Pirate Game with New Priorities
Replies: 6
Views: 1002

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...
by Poker
Tue Jun 20, 2017 1:38 pm UTC
Forum: Logic Puzzles
Topic: Pirate Game with New Priorities
Replies: 6
Views: 1002

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...
by Poker
Sat Jun 17, 2017 7:06 pm UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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 ...
by Poker
Fri Jun 16, 2017 1:38 pm UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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...
by Poker
Fri Jun 16, 2017 3:59 am UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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...
by Poker
Thu Jun 15, 2017 1:21 pm UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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 ...
by Poker
Wed Jun 14, 2017 9:27 pm UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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...
by Poker
Wed Jun 14, 2017 6:10 pm UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 1998

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...
by Poker
Sat May 27, 2017 3:33 pm UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

Re: Two more secrets

Yeah, it was. Fixed it.
by Poker
Fri May 26, 2017 2:58 am UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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...
by Poker
Fri May 26, 2017 12:12 am UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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 ...
by Poker
Thu May 25, 2017 11:57 am UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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...
by Poker
Thu May 25, 2017 4:08 am UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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 ...
by Poker
Wed May 24, 2017 9:33 pm UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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 ...
by Poker
Tue Apr 25, 2017 12:03 am UTC
Forum: Logic Puzzles
Topic: Two more secrets
Replies: 17
Views: 2683

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...
by Poker
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: 1478

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'...
by Poker
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: 1478

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 ...
by Poker
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: 1478

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...
by Poker
Wed Apr 05, 2017 6:37 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 3392

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...
by Poker
Sun Apr 02, 2017 4:01 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 3392

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, ...
by Poker
Fri Mar 31, 2017 6:50 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 3392

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 ...
by Poker
Fri Mar 31, 2017 4:58 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs
Replies: 12
Views: 7887

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, ...
by Poker
Wed Mar 29, 2017 3:27 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 3392

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...
by Poker
Sun Mar 26, 2017 10:58 pm UTC
Forum: Logic Puzzles
Topic: Pirate Game - A Variation
Replies: 1
Views: 1175

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 ...
by Poker
Sun Mar 26, 2017 1:44 pm UTC
Forum: Logic Puzzles
Topic: Situational Logic Puzzle
Replies: 5
Views: 1204

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...
by Poker
Thu Mar 09, 2017 10:14 pm UTC
Forum: Logic Puzzles
Topic: MisterGC's PUZZLES
Replies: 17
Views: 4192

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...
by Poker
Sat Dec 24, 2016 3:54 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Fri Dec 23, 2016 1:42 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Wed Dec 21, 2016 4:11 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Sat Dec 17, 2016 1:32 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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/...
by Poker
Fri Dec 16, 2016 7:41 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Fri Dec 16, 2016 3:35 pm UTC
Forum: Logic Puzzles
Topic: Word Puzzle.
Replies: 6
Views: 2158

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...
by Poker
Tue Dec 13, 2016 8:00 pm UTC
Forum: Logic Puzzles
Topic: Word Puzzle.
Replies: 6
Views: 2158

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...
by Poker
Tue Dec 13, 2016 2:45 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Sun Dec 11, 2016 7:43 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Sat Dec 10, 2016 4:02 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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.
by Poker
Fri Dec 09, 2016 4:31 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Fri Dec 09, 2016 2:44 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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. ...
by Poker
Fri Dec 09, 2016 1:53 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...
by Poker
Thu Dec 08, 2016 3:08 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 66384

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...

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