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Question

[1] Standard version of a classic

A king wishes to choose the man his daughter will marry.

She has three suitors: a Knight, a Knave, and a Commoner - whom the King wants to avoid.

The king does not know which man is which, and the suitors do not know each other.

But the king knows Knights always speak the truth, Knaves always lie; while Commoners respond as they please.

The king asks each man one yes/no question, then chooses the groom.

What are his questions, and how should he choose?

[2] Standard version with a twist

Now suppose the three suitors know each other.

Find a new strategy for the king to ask a question of just two of the three suitors to pick the groom.

[3] Making it a little harder

Find a strategy for the king to ask questions of only one suitor, but there can be two questions.

[4] The Puzzle Master special

Find a strategy for the king to ask only one yes/no question and only of one suitor.

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Edit for clarity: "ask questions of one suitor" means "ask one suitor a question"

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version 1]

He asks the same question for all three: "Are you a commoner?" and he shooses the one with the unique answer!

explanation:

Knight: "NO" < OBLIGATORY

Knave: "Yes" < OBLIGATORY

Commoner: YES or NO < Either one

So if he gets 2 NOs and 1 YES, the king should choose the unique YES and he would avoid the commoner

and if he gets 2 YESs and 1 NO, the king should choose the unique NO and he would avoid the commoner too.

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He asks the same question for 2 among them (A & B) about the third one ( C ): "Is C a Knave?"

4 Possibilities:

1-

A: "YES"

B: "YES"

==> The commoner is either A or B ==> C is definetely not a commoner

2-

A: "NO"

B: "NO"

==> The commoner is either A or B ==> C is definetely not a commoner

3-

A: "YES"

B: "NO"

==> The commoner is either B or C ==> A is definetely not a commoner

4-

A: "NO"

B: "YES"

==> The commoner is either A or C ==> B is definetely not a commoner

Explanation:

For 1 & 2, the fact that 2 people answered the same on that same question means that they cannot be a knight and a knave: they are either, a Knight and a Commoner, or a Knave and a Commoner. This means that at least one of them is a Commoner and C is the sure and safe choice.

For 3 & 4,

If C is a commoner, either A or B is a safe choice ==> Choose the guy who says YES

If C is the Knight, the Knave among A and B will say YES ==> Choose the guy who says YES

If C is the Knave, the Knight among A & B will say YES ==> Choose the guy who says YES

So for 3 & 4 choose the guy who says YES!

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Find a strategy for the king to ask questions of only one suitor, but there can be two questions.

Find a strategy for the king to ask only one yes/no question and only of one suitor.

What do you mean by of only one suitor...

Do you mean about only one suiter...?

or to only one suiter...? <= This is how I understood it first.

because this may mean that the answer I provided for version 2 is not suitable!

Thanks for clarifying...

Edited by roolstar
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But the king knows Knights always speak the truth, Knaves always lie; while Commoners respond as they please.

Does this mean the Commoner wants to be married to the Princess and would thus answer the best way that he thinks he could be married to her? Does he try his hardest to make sure the King picks him?

Or do you mean he basically answers randomly 'YES' or 'NO' for the purposes of this riddle?

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What do you mean by of only one suitor...

Do you mean about only one suiter...?

or to only one suiter...? <= This is how I understood it first.

because this may mean that the answer I provided for version 2 is not suitable!

Thanks for clarifying...

I mean "of" in the sense you mean "to".

The king asks one suitor two questions.

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Does this mean the Commoner wants to be married to the Princess and would thus answer the best way that he thinks he could be married to her? Does he try his hardest to make sure the King picks him?

Or do you mean he basically answers randomly 'YES' or 'NO' for the purposes of this riddle?

Well I think you can't trust him to answer in any way that you can anticipate.

but let's rule that out and assume nothing about his motivation - or that he has no motivation.

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Alright, thanks

I will get working on this

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Now suppose the three suitors know each other.

Is this for all the rest of the versions? [3] & [4]?

Sorry for all the question, but I just don't want to start on the wrong route......

Edited by roolstar
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other solutions"]

These could also work the same way:

Do you want to marry my daughter?

Are you a man?

Etc...

Basically any question where the Knight and Knave will give different answers guaranteed!

Edited by roolstar
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Ask A: "What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?" If the reply is NO, then B is definitely not a commoner. If the reply is YES, then C is definitely not a commoner.

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This seems to work:

Are you a Knave and is one of the others a Knight?

If you ask a Knight you will get a "NO"

If you ask a Knave you will get a "NO"

If you ask a Commoner you will get a "YES"

So if you get a NO choose the guy you asked...

If you get a YES just choose anyone of the remaining two!

Am I right?

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Is this for all the rest of the versions? [3] & [4]?

Sorry for all the question, but I just don't want to start on the wrong route......

Yes.

Assume they have full knowledge.

The phrase was added because #1 didn't require it.

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Ask A: "What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?" If the reply is NO, then B is definitely not a commoner. If the reply is YES, then C is definitely not a commoner.
You're asking A a question and then picking B or C. So if A is the commoner, you're home free.

If A is not the commoner, you're asking either

[1] what would a knight say a knave would say if ... or

[2] what would a knave say a knight would say if ... : either case, you get an untruth.

The "if" is "is C a commoner." So No means C is, and Yes means C isn't.

Nice job!

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This seems to work:

Are you a Knave and is one of the others a Knight?

If you ask a Knight you will get a "NO"

If you ask a Knave you will get a "NO"

If you ask a Commoner you will get a "YES"

So if you get a NO choose the guy you asked...

If you get a YES just choose anyone of the remaining two!

Am I right?

[1] The question is logically equivalent to the simpler question "Are you a Knave?"

Why? They share the same truth values in every case. The person asked is either a Knave or he is not a Knave,

[a] If he is a Knave then one of the others is a Knight, and the condition is true.

If he isn't a Knave then the condition immediately is false. [(False AND anything) is False.]

No problem, tho, both a Knight and a Knave will say NO, as you say. This point is just an observation.

[2] A Commoner may lie and say YES or tell the truth and say NO.

The OP says just the opposite: A commoner may replay as he pleases.

You say the Commoner cannot answer NO.

I don't think that conclusion is correct.

If you've thought of something I missed, let me know.

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Nice job!

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[1] The question is logically equivalent to the simpler question "Are you a Knave?"

Why? They share the same truth values in every case. The person asked is either a Knave or he is not a Knave,

[a] If he is a Knave then one of the others is a Knight, and the condition is true.

If he isn't a Knave then the condition immediately is false. [(False AND anything) is False.]

No problem, tho, both a Knight and a Knave will say NO, as you say. This point is just an observation.

[2] A Commoner may lie and say YES or tell the truth and say NO.

The OP says just the opposite: A commoner may replay as he pleases.

You say the Commoner cannot answer NO.

I don't think that conclusion is correct.

If you've thought of something I missed, let me know.

Actually "Are you a knave?" and "Are you a knave AND is one of the others a Knight?" are quite different:

In Are you a knave?:

1- The commoner has 2 options: Lie or tel the Truth

==>

Lie: YES

TRUTH: NO

This does not solve anything since you cannot always differentiate the answer from the KNIGHT and KNAVE's NO!

In Are you a knave AND is one of the others a Knight?":

1- A AND B means that a YES answer would have to be that A is a YES AND B is a YES!

2- The commoner has 2 options: Lie (IN BOTH STATEMENTS) or tell the Truth (IN BOTH STATEMENTS)

==>

LIE: YES & NO ==> NO

TRUTH: NO & YES ==> NO

And that was the mistake in my logic the first time!

And that made me realise that a commoner will either go all the way with his lies or the way with truths!

For that reason, he will always answer like a KNIGHT or a KNAVE would as he pleases...

And then sadly I also realised that

That meant that the KNAVE has to lie in all the statement:

"What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?"

The KNAVE will choose the COMMONER amongst B & C and apply the question to him!! And thus .........

And then I found a question that a knave cannot answer!!!

And I started this new thread! Knights, Commoners & Knaves (ORIGINAL)

I wrote this without a lot of focus and attention ( At least not as much as I give focus to other posts) not to mention that this does not solve the puzzle at hand

So please feel free to criticise my thinking process!

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Well I think what's happening is that a single question is being treated as if it were two questions.

In order to get information separately about

1. Are you a knave?

2. Is one of the others a Knight?

you'd have to ask two questions.

The OP requires you to ask only one question, which you did:

Are both 1. and 2. true?

That question has only a single response: Yes or No.

TT gives Yes.

TF, FT and FF give No.

Since TF is impossible [1 implies 2]

TT gives Yes.

F [with either T or F] gives No.

Same as if you just asked Is 1. true?

2- The commoner has 2 options: Lie (IN BOTH STATEMENTS) or tell the Truth (IN BOTH STATEMENTS)

==>

LIE: YES & NO ==> NO

TRUTH: NO & YES ==> NO

I would analyze the Commoner's freedom of response like this:

[1] The OP states the Commoner is free to answer as he pleases.

[2] If he had been asked two questions, he would not have to treat them the same. He could lie to one and tell the truth to the other if that pleased him.

[3] He wasn't asked two questions. The OP requires that only a single question be asked. That single question has a single answer. That answer is Yes or No, and the Commoner is free to choose which.

That meant that the KNAVE has to lie in all the statement:

"What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?"

The KNAVE will choose the COMMONER amongst B & C and apply the question to him!! And thus .........

I'm not sure what follows "And thus ........."

Here's my thinking about the Knave's response.

For every assignment of Knght/Knave/Commoner to A/B/C, SCHMOD54's question has a well-defined truthful answer.

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I agree 100% with you Bonanova...

The fact that the 2 statements are basically the same means that we will be in a TT or FF situation so I can drop any part of the question with no effect.

My reasonning behind the commoner answer for SCHMOD54 and the knave's response was also incorrect! What the heck was I smoking?

However this (The commoner can imitate a Knight or a Knave as he pleases) means that the only way to find a question that would work is to eliminate at least one of the suiters from the seclection process!!

And this is exactly what SCHMOD54 did!!!

Good job man!

BTW, we totally neglected Version [3]: basically because, if we can ask ONE question to find the suiter, why ask TWO??

Still it would be cool to know these 2 questions...

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However this (The commoner can imitate a Knight or a Knave as he pleases) means that the only way to find a question that would work is to eliminate at least one of the suiters from the seclection process!!

And this is exactly what SCHMOD54 did!!!

Good job man!

Thanks!

I wrote out all the permutations like so:

K = Knight, V = Knave, M = Commoner

A B C Response

K V M ?

K M V ?

V K M ?

V M K ?

M K V Y/N

M V K Y/N

And thought of what arrangement of Y or N for the ?s would allow to me to safely choose one of B or C... Alternating Y/Ns do the trick, i.e., any question where the knight and knave will have the same responses.

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Now, is there a way for the King to make sure that he gets the knight?

Both for Version 1 and where they all know each other. It would seem that this would be easier in the version where they know each other.

Working on it now.

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the commoner was motivated, he was a "suitor". He could have been after the kings money though.

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