Oneiromancer
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Scott wrote:
I'm not sure I understand what you mean about Gerry not being able to determine the question Oneiro.

I'm not sure what I mean either; that's why I'm confused. I decided to put the puzzle aside for a while because it was making my brain hurt. It works for DROD, who knows, it might work for this too.

But to try to explain a little better, in order for Gerry to answer Yes or No he has to know what Erik and Mike are going to answer. But you have to ask them the exact same question you are asking him. And then you have to worry about interpretations.

What I am trying to say is, say you point at Mike and ask Gerry, "Is that Erik?" He has to figure out what Erik and Mike would answer to the same question put to them. But if you point to Mike and ask Mike "Is that Erik?" that's a pretty odd question; you're more likely just ask him "Are you Erik?" In which case it's not the same question you are asking Gerry to figure the answer out to.

But since I'm trying to put this aside I don't know if this makes any more sense, perhaps you are right and it never did in the first place. Maybe someone else will understand what I am trying to say.

Game on,

____________________________
"He who is certain he knows the ending of things when he is only beginning them is either extremely wise or extremely foolish; no matter which is true, he is certainly an unhappy man, for he has put a knife in the heart of wonder." -- Tad Williams

Skylancer64
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Oneiromancer, Gerry would simply look at the question from Erik's point of view, then Mike's point of view. He would compare what those two would have answered, then formulate his answer using XOR. And in your example, Mike would answer the way he would. He would consider whether the person pointed at (himself) is Mike. And it would be. So he would lie and say No. Erik would say yes - the person pointed at is Mike. So Gerry would consider what Mike and Erik would have said. Since they would have said different answers, Gerry would answer yes.

The problem here is that for each question asked, you recieve a yes, or a no answer. Since two questions isn't enough to discern between 6 possibilities (2 x 2 < 6), all three questions must be used to determine the person. Three questions could theoretically choose between any of eight posibilities (2 x 2 x 2 = . However, another question must be used up to determine what yes/no is in their language. That means that one question must determine yes vs. no and help to identify who they are at the same time. However, a question that has helps to identify them must be answered differently by different people. (2 people would answer yes, and 1 would answer no, or vice versa). This is because a question all three would answer the same gives no new information. However, to discern bewteen yes and no requires all three same answers, as one can never be sure who is the one being asked. What's the way out of this paradox?

Hmmmmm....

I have a sneaking suspicion that there is a strategy that does not require distingushing yes from no...

[Edited by Skylancer64 on 01-03-2004 at 02:43 AM GMT]

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The_Red_Hawk
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You could do something where you use up all three questions then find out yes/no by looking at the order in which the person answered. I tried that, but keep ending up one short.

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Schik
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Oneiromancer wrote:
Actually, here's something I am confused about. Let's say you point to Erik and ask Gerry "Is he Mike?" How does Gerry interpret this? Is it like going up to each person and asking "Are you Mike?", in which case the answers would be No/No/No for Erik/Mike/Gerry, respectively, or is it like going up to each person and pointing to Erik and asking "Is he Mike?", which would give the answers No/Yes/Yes, assuming when you ask Erik you have to point to Erik. The problem is whether Gerry can really determine the correct question to answer in an XOR manner if it becomes impossible to ask the same question of all three people.

This has been addressed by others, but I figured I should throw an "authoritative" two cents in.

If you point to Erik and ask Gerry "Is he Mike?", then Gerry would consider how Erik would answer "Is he Mike?" and how Mike would answer "Is he Mike?" The fact that it sounds funny to ask Erik "Is he Mike?" while pointing at Erik is not important. In fact, Schik likes to talk about himself in the third person, so he's amused by this.

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Scott
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I can't come up with an answer do this but I did not that asking anyone "are you mike?" will let you know what the word for no is. I don't know if that will help anyone.

The_Red_Hawk
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I got it!!!!! (I hope).

I say to the first person, "If I ask Mike if Erik lies, what will he say? If he's Erik, he'll say yes, if he's Mike he'll say yes, and if he's Gerry, he'll say no.

If the first question's answer was no, he is Gerry, and I ask the next person "Is two and two four?" Yes = Erik, No = Mike, and I can find all three.

If the first question's answer was yes, I know that that person is Erik or Mike. So I say to the same person "Is two and two four?" Yes = Erik, No = Mike.

If the second question's answer was yes, I ask the same person if the next guy is Mike, and I will get the truth, and therefore can find all three.

If the second question's answer was no, I ask the same person if the next guy is Erik, and he will lie, and therefore I can also find all three.

[Edited by The_Red_Hawk on 01-03-2004 at 03:16 AM GMT]

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Avon
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How do you know if they are saying "Yes" or "No" given that you don't speak their language?

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"Les hommes ne sont jamais plus ingénieux que dans l'invention des jeux." -- Gottfried Wilhelm Leibniz

Schik
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The_Red_Hawk wrote:
I say to the first person, "If I ask Mike if Erik lies, what will he say? If he's Erik, he'll say yes, if he's Mike he'll say yes, and if he's Gerry, he'll say no.

Mike would actually say No there. The correct answer to "If I ask Mike if Erik lies, what will he say?" is YES. Mike will then lie and say No. You're kinda changing the question there depending on who happens to be asked.

If the first question's answer was no, he is Gerry, and I ask the next person "Is two and two four?" Yes = Erik, No = Mike, and I can find all three.

And then you're conditionally asking other questions dependent on what the answer to the first Q was, but you don't yet know what the words for Yes and No are.




____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

The_Red_Hawk
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Argh.

Can we please have a hint?

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

levelthirteen
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File: image.html (1.3 KB)
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If 'a' is the first reply you hear and 'b' is the other reply, then there are 4 possibilities:
aaa
aab
aba
abb
There are 6 different ways for them to be in the room (EMG,EGM, MEG,MGE, GEM,GME), so there is no mapping of replies that can reliably discern who is who.

DiMono
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It's done by creating instances of "if he's this person, then he must have replied this to the first question, but he didn't, therefor he can't be this person."

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Scott
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Its not enough to be able to say someone isn't this person though. You need to be able to say someone is this person. I can do this with 3 if I am lucky with 4 every time. I can't see a way to do it with 3 every time.

Oneiromancer
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Scott wrote:
I can't come up with an answer do this but I did not that asking anyone "are you mike?" will let you know what the word for no is. I don't know if that will help anyone.

I strongly implied this on the previous page, although I didn't really come out and say it.

Game on,

____________________________
"He who is certain he knows the ending of things when he is only beginning them is either extremely wise or extremely foolish; no matter which is true, he is certainly an unhappy man, for he has put a knife in the heart of wonder." -- Tad Williams

Watcher
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I got it! Except for one thing: my strategy requires you to know one of the words in advance. (Not what it means, just what it is.)

Okay, suppose the two words are bol and dok.

I walk up to the person in the middle, point to the person on the left, and ask "If I asked him 'Are you Erik?', would he answer bol?". Then I point to the person on the right and ask the same question.

Now, whoever the person I'm pointing to is, and whatever the question is, Erik and Mike will answer differently. Therefore, if I'm talking to Gerry, he'll say Yes both times.

Now, suppose bol means yes. Here's how people will answer:

Person I'm talking to/Person I'm pointing to
Erik/Mike: Mike will lie and say Yes, and Erik is honest about this, therefore he'll answer bol.
Erik/Gerry: Gerry will say No, and Erik is honest, therefore dok.
Mike/Erik: Erik will say Yes, but Mike will lie about this, therefore dok.
Mike/Gerry: Gerry will say No, but Mike lies, therefore bol.

Now suppose bol means no.

Erik/Mike: Mike will lie and say Yes, and Erik is honest, therefore he'll answer bol.
Erik/Gerry: Gerry will say No, and Erik is honest, therefore dok.
Mike/Erik: Erik will say Yes, but Mike will lie about this, therefore dok.
Mike/Gerry: Gerry will say No, but Mike lies, therefore bol.

Notice that the answers are the same, regardless of whether bol means yes or no.

Now, if I got the same answer twice, I'm talking to Gerry, and he just said Yes twice. Since I now know the words, I ask one of the other people "Does 2 + 2 equal 4?". If he answers Yes, it's Erik, if he answers No, it's Mike.

If I get two different answers, I'm talking to either Erik or Mike. Once I figure out which person it is, I'll know who the two other are (based on the answers to the first two questions, as above).

I ask the same person as before "If I asked you 'Are you Mike?', would you answer bol?". Both Erik and Mike will say No to the question "Are you Mike?"

Suppose bol means yes. If I'm talking to Erik, he'll be honest and say dok. If I'm talking to Mike, he'll lie and say bol.

Suppose bol means no, instead. Erik would be honest and say dok. Mike will lie and say bol.

Now that I know who the middle person is, I can figure out the two others, based on his answers to the first two questions. I still don't know whether bol means yes or no, though.

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Schik
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Watcher wrote:
I got it! Except for one thing: my strategy requires you to know one of the words in advance. (Not what it means, just what it is.)

Although your solution is different than mine, I believe it works except for what you noted. If you can get around that problem (Note: You can - it's pretty simple) then you got it!


____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Mattcrampy
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If only I had noticed that I don't know what they're saying... but then I got to make a MI:2 joke so it's all good.

Matt

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Watcher
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Schik wrote:

Watcher wrote:
I got it! Except for one thing: my strategy requires you to know one of the words in advance. (Not what it means, just what it is.)

Although your solution is different than mine, I believe it works except for what you noted. If you can get around that problem (Note: You can - it's pretty simple) then you got it!

Well, I've been thinking about this for a while, and I don't see how to get around the problem. It seems that whatever I do, I will sometimes have to ask three questions involving the words.

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Schik
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Watcher wrote:
Well, I've been thinking about this for a while, and I don't see how to get around the problem. It seems that whatever I do, I will sometimes have to ask three questions involving the words.

I'm thinking of two integers. Without knowing what either of them is, can you refer to one of them in some way?

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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Watcher
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Ah. Change "bol" to "that of your words for yes and no which comes first in alphabetical order" in the first two questions. For the third, I'll have heard both words, or not need to mention them.

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Schik
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Watcher wrote:
Ah. Change "bol" to "that of your words for yes and no which comes first in alphabetical order" in the first two questions. For the third, I'll have heard both words, or not need to mention them.

A well deserved win for Watcher. Now aren't you glad I didn't PM you the answer?

My solution went more like this:
Ask Person A: "Does the word for 'yes' come alphabetically before the word for 'no'?"

Erik will say whichever answer word comes alphabetically first. Mike will say whichever answer word comes alphabetically second. Gerry will say whichever answer word means 'yes'.

Ask Person A: "Does the word for 'no' come alphabetically before the word for 'yes'?"

If the answers to the two questions are the same, Person A is Gerry, and his answer means 'yes'. Ask Person B: "Is 2+2 equal to 4?" If his answer is the same as Person A's answers, he's Erik, otherwise he's Mike.

If the answers to the two questions differ and the answer to question 1 precedes the answer to question 2 alphabetically, he's Erik. If the answer to question 2 precedes the answer to question 1, he's Mike. Either way, you can use the "what would you say if I asked you..." trick to determine which of the other People is which.


____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

DiMono
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That was a really good puzzle. Did you come up with it, or is it one you grabbed from a site? (that looks a lot more cynical than I intended...)

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Schik
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That is not a Schik original. I saw it on a puzzle site somewhere, and it stuck with me. Most puzzles of that sort you'll see on about every puzzle site, but that one I've never seen again.

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The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi

Watcher
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Schik wrote:
A well deserved win for Watcher. Now aren't you glad I didn't PM you the answer?

Yes, I am.

Now, next puzzle:

You are given twelve metallic balls that look completely identical. Eleven of them weigh the same, but the twelfth is a bit heavier or a bit lighter. You are given a pair of balance scales, but you can't use any other weights than the twelve balls. Your task is, using the scales only three times, to find out which ball differs from the others, and whether it is heavier or lighter. How is this done?

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Mattcrampy
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I've heard this one, so I sit out.

Matt

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The_Red_Hawk
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First, put six balls on each side. The weight of each side is different, so take the heavier side off and weigh the other side three against three. Then, take two of the lighter three and weigh them. If they're equal, it's the third one, if not, it's the other one.

[Edited by The_Red_Hawk on 01-04-2004 at 03:57 PM GMT]

____________________________
Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.

.....the king of the skies.....

Mattcrampy
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But that odd one out could be heavier or lighter.

So you can't just take the heavier side.

I've just realised that although I know the question I've forgotten the answer, so I'll try and do it again. You'll all beat me anyway, but half the fun is trying to solve the puzzles on your own.

How sophisticated is our balance scale? Does it merely tell us if one side is heavier than the other, or can it tell us the proportions?

Matt

[Edited by Mattcrampy on 01-04-2004 at 04:21 PM GMT: Memory lapses]

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What do you call an elephant at the North Pole?

Watcher
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Mattcrampy wrote:
How sophisticated is our balance scale? Does it merely tell us if one side is heavier than the other, or can it tell us the proportions?

Only whether one side is heavier than the other.

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Today the refrigerator, tomorrow the world!

levelthirteen
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File: 3.txt (513 bytes)
Downloaded 95 times.
License: Other
From: Unspecified

You juggle the balls and see which one hits the floor. Then use the scale once to see if its heavier or lighter then the rest.


[Edited by levelthirteen on 01-05-2004 at 01:49 PM GMT: null]

DiMono
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I once used a similar one with 5 balls and 2 scale uses in a roleplaying campaign I ran. Nobody got better than an 80% chance solution, and they got gassed. This one's harder...

How about weighing 4 of them against 4 others. Then you swap one of the sets off for the remaining 4. You now know whether your objective ball is heavier or lighter, and in which set of 4 it is. Then you weigh that set 2 vs 2 and get it down to a 50% chance. Hmm...

Weigh 5 vs 5. Then remove 2 from one side, move another 2 from the other side to make up the loss, and put the 2 left out on the second side. If it balanced the first time, then it's one of the 2 remaining, and which direction the scale tips the second time will tell you if the ball's lighter or heavier. If it didn't balance the first time, but balanced the second time, same thing. If it tilted one way the first time and the other way the second, then it's one of the 2 you moved over, and the same thing happens. If it tilted the same way each time, then you're down to six balls and 1 scale use. I think the best thing to do then is rotate two balls around in the same fashion again, but that also just gets you down to a 50% chance at the end.

Alright, so neither of those worked, but am I on the right track?

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Schik
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DiMono wrote:
Alright, so neither of those worked, but am I on the right track?

Not for the solution I know. I really want to start giving hints, as this is a toughie, but I'll leave that to Watcher if he so desires.

____________________________
The greatness of a nation and its moral progress can be judged by the way it treats its animals.
--Mahatma Gandhi