## Search found 135 matches

Sun Jun 30, 2019 12:15 pm UTC
Forum: Logic Puzzles
Topic: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"
Replies: 17
Views: 2223

### Re: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"

[quote="benkoren"] You not payng attention[/quote] Well, look who's talking! My solution (and phlip's one, as it is virtually the same) is perfectly valid, but as you seem to be purposefully refusing to understand it, I won't explain it over and over again. Fine by me.
Sat Jun 29, 2019 7:47 pm UTC
Forum: Logic Puzzles
Topic: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"
Replies: 17
Views: 2223

### Re: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"

You state further that "If X is false, then the sentence is paradoxical." Why? The sentence can either be true or a lie there is no third option and robots have no reason not to respond. No, it is neither true nor false: as you pointed out yourself, if X is false, then the statement "...
Sat Jun 29, 2019 7:17 am UTC
Forum: Logic Puzzles
Topic: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"
Replies: 17
Views: 2223

### Re: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"

You will get an answer to this question but in essence you just asked “is A is robot 1?”. No, I will get an answer if the statement is true, and no answer if the statement is false. Because if the statement is false, then both answers to the question are self contradictory. The confusions in the re...
Thu Jun 27, 2019 2:22 pm UTC
Forum: Logic Puzzles
Topic: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"
Replies: 17
Views: 2223

### Re: Logic Puzzles. “3 ROBOTS” - harder than "Hardest Ever"

My first step would be to find a meta question that allows to map true or false to the light bulb lighting up or not. The meta sentence applied to a true proposition can have an answer, but when applied to a false proposition, it must be paradoxical. For that, the sentence can refer to its own trut...
Fri Nov 30, 2018 3:54 pm UTC
Forum: Logic Puzzles
Topic: Rome
Replies: 1
Views: 1811

### Re: Rome

As I understand it, it is the classic switch puzzle, (http://forums.xkcd.com/viewtopic.php?f=3&t=73 http://forums.xkcd.com/viewtopic.php?f=3&t=13669 http://forums.xkcd.com/viewtopic.php?f=3&t=69986), the unlocked door playing the role of the switch. If we can't count on the room to stay ...
Mon Nov 26, 2018 1:15 pm UTC
Forum: Logic Puzzles
Topic: Poker
Replies: 1
Views: 1770

### Re: Poker

Brutally arithmetical solution: Call A, B and C the number of coins each initially takes, translate what we know into three equations (for example, 2B/3+42 = (A+B+C)/3, because after Paul removed 1/3 of his initial stock and getting 42 coins back, he has 1/3 of the total), then solve...
Tue Nov 20, 2018 9:37 am UTC
Forum: Logic Puzzles
Topic: Protection fee
Replies: 2
Views: 2170

### Re: Protection fee

Spoiler:
As the 24 dollars just go from one bag to the other, so the leader simply took five bars out of the 50 bars present, which is a fee of 10%.
Now, as the fee for 32 bars is 3 bars and 24 dollars, 24 dollars is the value of 0.2 bars, therefor a gold bar is worth 120 dollars.
Tue Nov 20, 2018 9:31 am UTC
Forum: Logic Puzzles
Topic: Penalty fee
Replies: 1
Views: 1832

### Re: Penalty fee

Calling x the smallest number, the others are x+1 and x+2, so the sum of all three is 3x+3 and the product is x*(x+1)*(x+2) = x^3+3x²+2x. So we need to solve x^3+3x²+2x-(3x+3) = 0, which is x^3+3x²-x-3 = 0. 1 and -1 are trivial solutions, we easlily get to this: The three va...
Sun Nov 11, 2018 2:12 pm UTC
Forum: Logic Puzzles
Topic: Last Call
Replies: 1
Views: 1858

### Re: Last Call

So, if I get the explanations correctly, there are 6 oarsmen including me, their crossing times are 5, 10, 25, 30, 30 and 30 minutes. That is, assuming I can still able to row the boat, which doesn't seem to be very clear. Again, it seems implied that the boat can be handled by a single oarsman when...
Tue Nov 06, 2018 9:48 am UTC
Forum: Logic Puzzles
Topic: Sacrifice
Replies: 8
Views: 6468

### Re: Sacrifice

Go back to your smartass solution for a second - there's more to be done there to get a solution with at most 4 chicken risked, and if you're lucky you lose none But then, we can do better, with the "break the game" solution: Take one chicken, make it sip from the first canister. If it di...
Thu Apr 19, 2018 9:57 am UTC
Topic: 1982: "Evangelism"
Replies: 109
Views: 27221

### Re: 1982: "Evangelism"

fibonacci wrote:If you point a telescope out to the right off the edge of the chart, on a clear night you can spot "Vegans".
"Oh, Hey, I didn't see you guys all the way over there" should have been the punchline.
https://xkcd.com/435/
Fri Feb 02, 2018 8:59 am UTC
Forum: Logic Puzzles
Topic: The Goddess, the Villagers, and the Traveler
Replies: 16
Views: 9343

### Re: The Goddess, the Villagers, and the Traveler

Cradarc wrote:The only exception is if you put in additional limitations to what the villagers can do which are not stated in the problem.
Well, the villagers are supposed to have the power to selectively erase information from their own memory on command. Forget about limitations not stated in the problem.
Wed Jan 31, 2018 10:04 am UTC
Forum: Logic Puzzles
Topic: The Goddess, the Villagers, and the Traveler
Replies: 16
Views: 9343

### Re: The Goddess, the Villagers, and the Traveler

I have something that is not very satisfying because it implies that the villagers are very gullible, but it doesn't require magically or hypnotically removing information they already have. Just updating it in a way you control, so that every time they change their mind, they actually have more inf...
Tue Jan 30, 2018 8:54 am UTC
Forum: Logic Puzzles
Topic: The Goddess, the Villagers, and the Traveler
Replies: 16
Views: 9343

### Re: The Goddess, the Villagers, and the Traveler

Actually that is a completely valid command to give. You can ask the villagers to forget and remember any bits of information on a whim so long as it's in the form of command and follows in accordance with the three rules set for them I have a real problem with this. Forgetting something on command...
Fri Jan 26, 2018 11:50 am UTC
Forum: Logic Puzzles
Topic: The Goddess, the Villagers, and the Traveler
Replies: 16
Views: 9343

### Re: The Goddess, the Villagers, and the Traveler

There's something that I don't get here. Please consider this first theoretical situation: The goddess actually is just a phantom flying around the village. She is not specifically linked to any of the villagers. The villagers think that she is walking among them, but they're wrong. apart from that,...
Mon Oct 16, 2017 12:17 pm UTC
Forum: Logic Puzzles
Topic: Could there still be new hat puzzles?
Replies: 12
Views: 10505

### 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...
Mon Oct 09, 2017 2:40 pm UTC
Forum: Logic Puzzles
Topic: Could there still be new hat puzzles?
Replies: 12
Views: 10505

### 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 ...
Wed Sep 27, 2017 1:03 pm UTC
Forum: Logic Puzzles
Topic: Could there still be new hat puzzles?
Replies: 12
Views: 10505

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

An absurd strategy where the prime-numbered players (2,3,5,7) pick the minority color and the other players pick the majority color As I said in the OP, "They can devise a strategy, but it can't be nominative. The player's can't take into account their own identity, the whole strategy has to b...
Thu Sep 21, 2017 4:05 pm UTC
Forum: Logic Puzzles
Topic: Could there still be new hat puzzles?
Replies: 12
Views: 10505

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

HonoreDB wrote:This fails for one of the two most common splits, and doesn't use relative positions, so it's probably not optimal.
It is a good start, but you are right, it is possible to get less than half this error rate.
Tue Sep 19, 2017 3:17 pm UTC
Forum: Logic Puzzles
Topic: Could there still be new hat puzzles?
Replies: 12
Views: 10505

### Could there still be new hat puzzles?

Here's a hat puzzle inspired by this one . Seven perfectly rational players stand in a circle. Everyone gets assigned, randomly and independently, a black hat or a white hat. Nobody can see the color of his own hat but the colors of all other players. All the players must try to guess the color of t...
Tue Sep 19, 2017 11:34 am UTC
Forum: Logic Puzzles
Topic: Another hat puzzle
Replies: 9
Views: 6861

### Re: Another hat puzzle

I don't have a formal proof that this will work for any n>2, but it worked smoothly for the values I tried, and it seems that increasing n just gives more margin of error when you build the strategy. Here it is: First, I have to determine in advance the lower bound of the number of correct guesses. ...
Wed Sep 06, 2017 8:20 am UTC
Forum: Logic Puzzles
Topic: 538 hats riddle
Replies: 20
Views: 8731

### Re: 538 hats riddle

It may be possible to do better with two rules than SirGabriel has with one, but your posted win rate is less than his. To keep the thread alive, I think it is relevant to confirm that it is indeed possible to do better than SirGabriel, under the assumptions pointed out by jaap. For any number of p...
Wed Apr 12, 2017 1:12 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 10139

### Re: Two secrets

I think I have an O(log(N)) solution. Let A initially be {1, 2, 3, ..., N-1}. At all times, we know that at least one of the numbers is in A. Divide A into three roughly equal sets A 1 , A 2 , and A 3 , and ask about A 1 ∪ A 2 , A 1 ∪ A 3 , and A 2 ∪ A 3 . If we get a "yes" response to on...
Wed Apr 12, 2017 9:40 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 10139

### Re: Two secrets

Ok, I took a chance to work on my solution again, even if now it is just a correction of Nitrodon's solution, but here is where I landed: Let the initial state be state I, where we have one set containing both numbers. We cut the set in n parts and test every pair of parts. If there is only one yes,...
Wed Apr 12, 2017 8:31 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 10139

### Re: Two secrets

I think I have an O(log(N)) solution. Let A initially be {1, 2, 3, ..., N-1}. At all times, we know that at least one of the numbers is in A. Divide A into three roughly equal sets A 1 , A 2 , and A 3 , and ask about A 1 ∪ A 2 , A 1 ∪ A 3 , and A 2 ∪ A 3 . If we get a "yes" response to on...
Mon Apr 03, 2017 9:53 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 10139

### 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 1:02 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 10139

### 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 ...
Wed Jan 18, 2017 10:33 am UTC
Forum: Logic Puzzles
Topic: New puzzle : Equalize
Replies: 13
Views: 6190

### Re: New puzzle : Equalize

a solution is impossible for the following example "random" starting position: r r bb bb r r rrrr rbbr rbbr rbbr gives 1 1 1 1 1 -2 -2 1 -1 2 2 -1 -1 1 1 -1 with the original system, and 2 3 3 2 3 3 3 3 2 5 5 2 1 3 3 1 with yours. In the first case, both sums are 2, in the second case bot...
Wed Aug 05, 2015 2:28 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### Re: the halting problem

Change your definition of x to this. x takes just one input, and: x(p) internally uses h and works this way: -if program p halts with input p, loop forever -if program p does not halt with input p, return 1 Now x(x) halts if and only if x(x) does not halt. There is an important point here: this is ...
Wed Aug 05, 2015 1:55 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### Re: the halting problem

It sounds like you're not familiar with quines , which are programs that can print their own source code. Well, I actually am, wrote one years ago in C, discovered recently that it was possible with compressed files too. The very last part is the one that really blew my mind. I mean, the fact that ...
Wed Aug 05, 2015 1:43 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### Re: the halting problem

I'm not sure where you got this proof from, but the explanation on Wikipedia seems pretty clear to me (and different from yours). Well, from various places, including the wikipedia article. Can you tell me how it is different from mine ? Wikipedia's h is the same as my h, my x(i,i) would be wikiped...
Wed Aug 05, 2015 1:24 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### Re: the halting problem

For example, you could be passing x as a string (the source code), and x-as-a-program runs some checks on the string to decide whether it halts or not. Ok, but with what inputs? By definition, x halts or not depending on its input. Here, x is supposed to decide wether x halts or not. But with which...
Wed Aug 05, 2015 1:06 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### Re: the halting problem

That is a function that does not use its input. What does it have to do with my question?
Wed Aug 05, 2015 12:16 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7850

### the halting problem

Hello I apologize in advance for how trivial this may seem for anyone that truly understands the halting problem and/or if this question has already been answered here, but my searches were not conclusive. There is something I don't get in the halting problem, and none of the explanations I've read ...
Fri Apr 24, 2015 7:22 am UTC
Forum: Logic Puzzles
Topic: Simple math word puzzle
Replies: 9
Views: 3010

### Re: Simple math word puzzle

I would prefer from any student to see the full solution. 1. y=x+20 2. xy=wz+d 3. z=w+26 4. x+y=w+z Putting 1 into 4 4a. 2x+20 = w+z Putting 3 into 4a 4b. 2x+20=2w+26 ---------- -26 4c. 2x-6=2w --------------- /2 5. x-3=w Putting 1 into 2 2a. x(x+20)=wz+d Putting 3 into 2a 2b. x(x+20...
Thu Apr 23, 2015 11:49 am UTC
Forum: Logic Puzzles
Topic: Simple math word puzzle
Replies: 9
Views: 3010

### Re: Simple math word puzzle

Here's my method:

Spoiler:
The two pairs of integers have the same sum, so they have the same arithmetic mean, x.
The first two numbers are x-10 and x+10, the two other are x-13 and x+13.
The first product is x²-100, the second one is x²-169.
The difference between the products is 69.
Tue Feb 03, 2015 12:30 pm UTC
Forum: Logic Puzzles
Topic: Six statements. How many are true?
Replies: 20
Views: 7410

### Re: Six statements. How many are true?

Of course I solved tis with the classic method, but considering how some of the statements were designed, I wanted to try something else. I consider the nature of a statement depends only on how this statement matches reality, and not on what other statements say about it. For example "This sta...
Mon Dec 17, 2012 6:00 pm UTC
Forum: Logic Puzzles
Topic: Create a perfect lossless compression algorithm
Replies: 21
Views: 5208

### Re: Create a perfect lossless compression algorithm

Does Alice have a way of telling Bob the transfer is over, or do we need to establish a protocl which allows Bob to know when he has read the last bit, and stop expecting new information from Alice ? If Bob can know when the transfer is over wothout having to figuring it out with the data, then we c...
Mon Oct 29, 2012 5:26 pm UTC
Forum: Logic Puzzles
Topic: (Hopefully) new balance puzzle
Replies: 7
Views: 2732

### Re: (Hopefully) new balance puzzle

Thank you for proving me that this can be solved with a non computer-enhanced brain!
Mon Oct 29, 2012 10:07 am UTC
Forum: Logic Puzzles
Topic: (Hopefully) new balance puzzle
Replies: 7
Views: 2732

### Re: (Hopefully) new balance puzzle

Snark: I think we're supposed to specify all three trials in advance, before we have the results of any of them. Here's my solution, retaining your labeling of the coins as ABCDEFG: Test ABC vs. DEF, AD vs. BE, and AF vs. CD. ABC < DEF, AD < BE, AF < CD: AG are fake ABC < DEF, AD < BE, AF = CD: AC ...