disoriented
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Have these been posted here yet?

Part 1:

Part 2:

Edit: ok, I see the banana one was posted before at least.

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[Last edited by disoriented at 03-20-2015 10:45 PM]

Someone Else
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For the second one, it's a similar solution. All the trucks travel 100/50=2 miles, then you rearrange the gas and continue. Then you rinse and repeat.
Wolfram Alpha says that:
sum from n=1 to 50 100/n
is 449.9, or approximately 450 miles.

jamesdenem
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Someone Else, while your concept is the key to solving how far they go, there is a flaw in your answer. Using the concept you stated, I am currently working on getting the crate as far as I can, and have gotten past 450 miles with trucks to spare at full tanks.

I will post my solution once I work it out.

EDIT: Nevermind. I just caught my error in my thinking and realize that Someone Else does have the correct answer.

EDIT2: It is implied the trucks must start from the same place, otherwise you could have your "fleet" situated with each truck 100 miles from each other with full tanks and get the non trivial solution of 5000 miles

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[Last edited by jamesdenem at 03-21-2015 12:35 PM]

jamesdenem
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Since there has been nothing posted here for a while, why don't I get the ball rolling with this puzzle:

An unnamed smitemaster has need of a mimic potion to clear a particularly devious hold.
While searching for a merchant who could sell him one, he overhears the following conversation:
"I found some merchants who seem to be crazy, they are selling potions for practically nothing."
"Why didn't you buy any then?"
"These three merchants are a strange bunch. They are set up next to each other in a line and you can't even tell them apart, they look so alike."
"It sounds like one merchant who used a mimic potion twice to me..."
"Perhaps, but the strange thing is; to do business with any of them, you have to approach one of them and ask him a yes or no question."
"Why is that strange?"
"Because one of them always tells the truth, another always lies, and the third seems to randomly choose either the truth or lying. I have watched them for a while, and as far as I can tell, the same man is never in the same place."
"What does it matter?"
"Because after watching them for a while, I have discovered that the merchant who chooses randomly between truth and lying has all of his potions poisoned."

Now, the unnamed smitemaster considered himself to be pretty intelligent, and felt that the deal for the potion was too great to pass up. (Especially since he didn't have much on him)
He found the merchants, and after thinking carefully approached one and asked his question.

What question did the smitemaster ask to ensure that he would not get a poisoned potion?

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disoriented
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[Last edited by disoriented at 03-31-2015 07:16 PM]

jamesdenem
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jamesdenem wrote:
... you have to approach one of them and ask him a yes or no question."

This would invalidate your question.

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Aquator
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I believe I found a question that solves the problem, but I pretty much got there the dumbest way possible. I won't answer because I don't think my line of thinking really counts as properly solving the logic behind this puzzle.
That, and I'm also terrible at coming up with puzzles myself.

Here's what I did, in case anyone wants to know and/or needs a little hint themselves.

Lucky Luc
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I'm not very serious, of course. Except if that was the answer you were looking for. Then I'm dead serious.

My reasoning:

EDIT: Oh, sorry, post collision. (yeah, I needed a while to sort out my thoughts )

EDIT 2: Oh, huh. I've made the wrong assumption , which means that there's probably a less cheesy solution than mine. Still, I wonder what you think of it .

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[Last edited by Lucky Luc at 03-31-2015 11:35 PM]

Aquator
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Lucky Luc wrote:

Click here to view the secret text

×If the merchant's head explodes while they're trying to resolve that paradox, grab a few potions and run away before someone sees you.

Click here to view the secret text

×(my head exploded while I was trying to figure it out)

Lucky Luc is the merchant whose potions the Smitemaster should take.

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[Last edited by Aquator at 04-01-2015 12:43 AM]

jamesdenem
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Lucky Luc wrote:

Click here to view the secret text

×"Will your answer to this question be the same as if I asked you whether 1+1=3?"
(a simple "Could you answer this question with no?" would suffice here)

The question you came up with could also be interpreted as follows:

That kind of question can be answered by each merchant.

Lucky Luc wrote:
So we have to present them a paradox.

Typically when a truthteller or liar is presented with a paradox in the context of a puzzle, they won't answer the question, rather than risk having their heads explode.
Also, I mentioned that the random answerer doesn't just simply answer "yes" or "no" randomly, but chooses between truth or lies, so essentially answers questions asked as if he were one of the other two, chosen at random.

I did think your "solution" was somewhat unconventional, which is usually what is needed to solve these type of puzzles.

Do be careful when thinking of paradoxes, though. They tend to be confusing things.

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blorx1
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I don't have another puzzle, but I'm pretty sure I have a solution. I ended up resorting to truth tables so my question is a bit of a mess, but it should work, assuming that the lying people just invert a truthful answer to questions.



I kind of hope I'm wrong so there's no pressure to think of or find any clever puzzles.

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skell
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It's a pretty ordinary twist on the classic knights & knaves puzzles. If you've done any of Smullyan's books it shouldn't be too hard to come up with a correct answer. I did his books but it was over 10 years ago so I don't feel like figuring it out if other people already did it .

Random Trivia: Raymond Smullyan has released his latest puzzle book in the age of 94. I wonder how much more is he going to write!

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Aquator
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Nuntar
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blorx's solution is very interesting. In Raymond Smullyan's knight-knave-normal problems, Smullyan assumes that a normal can freely give any answer, which would make this solution invalid. However, if normals are required to give an answer that is either true or false, this solution works.

Another Smullyan problem is: Given that you are a native of the island and you are not normal, what statement you could make that would convince someone you are not normal? With the Smullyan definition of normals, there is no solution. With blorxian normals, there would be.

Aquator's solution is the standard one. You don't have to use the fact that they are positioned in a line, but you are expected to be able to refer to them individually, and position is the simplest way of doing this.

I set a puzzle equivalent to this back on page 72.

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blorx1
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I suppose I forgot about the fact that even though the random guy is giving you garbage, he's only doing it when you're talking to him, which really only proves that you can't drink the potion of the merchant you're talking to (without assuming what I did). Of course, my solution would probably cause most puzzles like this to just boil down to truth tables like the way I answered it.

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jamesdenem
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Blorx1's question will work, as I will explain next.


That is the interesting result of these kinds of puzzles. There can possibly be other solutions to the "intended" one if you know your way around truth tables, and can figure out what you are trying to get to.

Aquator has the correct reasoning about the type of question to ask, and his would work as he says.



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Lucky Luc
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jamesdenem wrote:
Also, I mentioned that the random answerer doesn't just simply answer "yes" or "no" randomly, but chooses between truth or lies, so essentially answers questions asked as if he were one of the other two, chosen at random.

Oh, that's clever! Yup, I didn't read that carefully enough. Considering that, both the intended solution and that of blorx1 are extremly clever.

jamesdenem
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Might as well post this simple logic puzzle, then.
I don't expect it to last too long...

You are travelling in the land of truthtellers and liars.(A person either always tells the truth or lies)
You come across a sign warning travelers that there is a fork in the road ahead, and one of the paths lead to extremely deadly danger.
Unfortunately, the sign makes no mention of which path it is.
Coming to the fork, you see there is a native standing there.
You are in a hurry, and have time to ask him only one question.

What do you ask him to ensure that you go down the safe path and not the deadly one?

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Tamsk
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Ask him to leave by one of the two paths.

Aquator
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Realize that you've made a big mistake coming to an entire nation of insane bipolar puzzle people while expecting to get anything done in a timely manner.

Once you've done that, stand next to the native and wait for the next traveler coming this way. If he asks you something just answer randomly.

After the traveler has chosen a path, wait for half an hour. Take note of any terrified screams of agonizing pain. If you hear any, you're probably better off taking the other path. If you don't, follow the same path as the traveler before you, knowing that the worst that could happen, a mercifully short death, is probably still better than journeying through a country where an innkeeper might force you to solve a puzzle determining whether you'll wake up with both of your kidneys or not.

TripleM
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The fact that "If I were to ask you X, what would you say?" always results in a truthful answer to X tends to solve most of these puzzles pretty easily.

Aquator
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TripleM wrote:
The fact that "If I were to ask you X, what would you say?" always results in a truthful answer to X tends to solve most of these puzzles pretty easily.

In case you were referring to me saying that it's probably not that great to be somewhere where your life constantly depends on your ability to solve logic puzzles, I was assuming that the puzzles would not always be the same and could be of higher complexity.

I'm pretty sure using the whole "some people always lie and some always tell the truth" setup, you could potentially craft Boolean puzzles of any complexity.

TripleM
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Nah, wasn't a direct response to you - just a method that gives you an easy solution to both these puzzles and most similar ones:

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[Last edited by TripleM at 04-07-2015 02:05 AM]

Rabscuttle
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A: The sign was written by a liar. Both paths actually lead to deadly danger, so you should turn around and go back the way you came.

jamesdenem
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TripleM has the correct answer, which as I said was pretty simple.

Usually these types of logic problems ignore common sense.
For example, how would a group of tourists find themselves in a situation where they wanted to cross a river while bunched with an equal number of cannibals.
You would think either the cannibals would get more of them, would overpower them, or the tourists would be smart and stay with their group...


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RoboBob3000
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A particular, unusual island is populated entirely by truth-tellers and liars, all outwardly identical.

The truth-tellers, bound by their blind adherence to their strict moral code, exclusively tell the truth. Their unflinching honesty is one of their many shortcomings. When asked for the truth, they unquestionably provide the truth, and it's always the whole truth. Often more truth than necessary. The idea of the secret is foreign to them. Their brutal honesty fails them in their personal relationships, causing them to come across as gruff and matter-of-fact with their unwanted criticisms of others when in fact they mean well. They are often taken advantage of. Their credit card numbers are taken. Everybody knows where their spare house key is hidden.

The liars have it no easier. Being put off by the lives they perceive the truth-tellers to live, the liars have reached the flawed conclusion that all truth is problematic, and as such have taken a hard-line stance against it and always exclusively tell lies. This behavior also stems from their general insecurities - they worry that their particular truths about themselves wouldn't represent them well, and would rather paint a rosier picture of things with a simple fib or a slight exaggeration. Communication with the liars on the island is difficult and tiresome. They are unable to hold steady employment.

Life is hard here.

All of the truth-tellers and liars on the island have been gathered into three enormous boxes. One box contains only truth-tellers, one contains only liars, and one contains a mix of both. The three boxes are labeled TRUTH-TELLERS, LIARS, and MIX, but each box has an incorrect label applied to it.

You have been hired for a small fee to fix the labels on the boxes. Your employer has asked you not to concern yourself with the purpose of these boxes. It is not your job to worry about the ethics of this situation - there are higher-ups who do that. Your job is to fix the labels.

You do have some misgivings about the whole thing, but you need the money, so you figure that now isn't the time to cause waves. Maybe if you get invited to relabel boxes again in the future you'll ask a few more questions. For today, you're just going to see how this shakes out.

You can extract a person from a box whenever you like to ask them what they would say if you asked them if they were a truth-teller or a liar. What is the fewest number of people you need to query in order to correctly label the boxes?

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Nuntar
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Heh. A nice blend of two classic problems. This one is really easy:

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Nuntar
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Place a penny on a flat surface. Place a second penny exactly on top of it, then move it north until the pennies no longer overlap, but just touch. Place two more pennies on top of the first two, then move them east until the pennies no longer overlap, but just touch. The space in between the pennies now forms a four-pointed star with curved arms. Draw the largest possible circle inside this star, just touching each penny. What is the ratio of its radius to the radius of one penny?

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Lucky Luc
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I'm not gonna answer it because I've done this so many times before, and I wouldn't know which puzzle to post next, anyway.

Pearls
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Hey, w-wait, that's the guy who shamelessly promotes his own...

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[Last edited by Pearls at 04-09-2015 09:46 PM]