[Guest]

Each inhabitant of an island are either a truthteller who always speak the truth, or a liar, who always speaks falsely.

Three boys P, Q and R who live in that island, are each either a truthteller, or a liar. It is known that P, Q and R together have 6 marbles. A passing visitor asked them how many marbles each had, to which P responded that he had only 1 marble, and Q responded that P had 2 marbles, while R said that P had more than 3 marbles. However all the three boys agreed that Q had precisely two marbles..

If each of the three boys had at least 1 marble, determine the respective number of marbles possessed by each of the three boys.

[Pickett]

Each inhabitant of an island are either a truthteller who always speak the truth, or a liar, who always speaks falsely.

Three boys P, Q and R who live in that island, are each either a truthteller, or a liar. It is known that P, Q and R together have 6 marbles. A passing visitor asked them how many marbles each had, to which P responded that he had only 1 marble, and Q responded that P had 2 marbles, while R said that P had more than 3 marbles. However all the three boys agreed that Q had precisely two marbles..

If each of the three boys had at least 1 marble, determine the respective number of marbles possessed by each of the three boys.

So, basically we know that R HAS to be a liar...because if he was telling the truth, then P would have at least 4 marbles, and Q would have 2...which means that he couldn't have any...so if R is a liar, we know that all of them are liars....because ALL of them said that Q has 2 marbles (including R, which we've shown must be a liar)...

If all of them are liars, then P can't have 1, 2, or more than 3 marbles, Q can't have 2 marbles, and R would have the rest:

P has 3 marbles

Q has 1 marble

R has 2 marbles

[HoustonHokie]

They're all liars. That's the only way they could all disagree about P, but agree about Q. So, P has 3, Q has 1, and R has 2.

[Guest]

Since they all agreed, they have to be all lying or all telling the truth. Obviously, it can't be truth, because their initial responses don't agree with each other. Taking all responses together, P cannot have 1, 2, or >3 marbles, so it must be 3. Q cannot have 2, and since Q and R both have to have at least 1, it leaves 1 for Q and 2 for R.

P = 3

Q = 1

R = 2

[Gmaster479]

See everyone elses answer to see what I got.

[Guest]

Each inhabitant of an island are either a truthteller who always speak the truth, or a liar, who always speaks falsely.

Three boys P, Q and R who live in that island, are each either a truthteller, or a liar. It is known that P, Q and R together have 6 marbles. A passing visitor asked them how many marbles each had, to which P responded that he had only 1 marble, and Q responded that P had 2 marbles, while R said that P had more than 3 marbles. However all the three boys agreed that Q had precisely two marbles..

If each of the three boys had at least 1 marble, determine the respective number of marbles possessed by each of the three boys.

P has 3 marbles, Q has one marbles and R has two marbles

[Guest]

I believe this is an easy problem. (I hope I am right).

First of all we have to notice that all of the guys agree on a sentence and since a sentence can not be truth and lie at the same time then we only have to possible cases, either they are all liars or they are all truthtellers.

So let's check both possibilities:

They are all truthtellers:

This leads to an inconsistency because P says that he has only 1 marble and Q says that P has 2 marbles. So they can not be both truthteller.

They are all liars: (This is the correct answer)

Now, we know that they are all liars so we must now find out how many marbles they have.

P is a liar and he said that he has 1 marble. So, P DOES NOT HAVE 1 MARBLE.

Q is a liar and he said that P has 2 marbles. So, P DOES NOT HAVE 2 MARBLES.

R is a liar and he said that P has more than 3 marbles. so, P HAS 3 OR LESS MARBLES

Therefore:

P has 3 or less marbles, but hi doesn't have 1 and he doesn't have 2 and we know that everyone has at least 1 marble so the only possibility is that P has 3 marbles.

Now lets go for the other two.

Q is a liar and he said that he has 2 marbles. So, Q DOES NOT HAVE 2 MARBLES.

Now there are only 3 marbles left (because P has the other 3). So either Q has 1 marble or 3 marbles.

But Q cannot have 3 marbles because then R would have 0 marbles. Therefore the only possibility is that Q has 1 marble.

And then R = 6 - P - Q = 6 - 3 - 1 = 2

So the answer is:

P has 3

Q has 1

R has 2

Sengupta, am I right?.