10 replies to this topic

[33724]

Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce
any truth from any set of axioms. Two integers (not necessarily unique) are
somehow chosen such that each is within some specified range. Mr. S.
is given the sum of these two integers; Mr. P. is given the product of these
two integers. After receiving these numbers, the two logicians do not
have any communication at all except the following dialogue:

<<1>> Mr. P.: I do not know the two numbers.
<<2>> Mr. S.: I knew that you didn't know the two numbers.
<<3>> Mr. P.: Now I know the two numbers.
<<4>> Mr. S.: Now I know the two numbers.

Given that the above statements are absolutely truthful,
what are the two numbers?

[The Dirty Filipino]

4,13.
or
13,16.

Edited by T.E.I., 25 November 2008 - 10:58 AM.

[33724]

well that was quicker than expected.

could you use spoiler []'s nextime.




A logician vacationing in the South Seas finds himself on an island inhabited by two tribes. One of liars, and one of truth-tellers. Members of one tribe always tell the truth and members of the other tribe always tell lies. he comes to a fork in the road and has to ask a native bystander which branch he should take to reach a village. he has no way of telling if the native is a truth-teller or a liar. The logician thinks for a moment, then asks one question only. From the reply he knows which road to take. What question does he ask?

[phalkon]

Spoiler! --Click here to view--

this may not be right, but i'd first figure out the directions on a compass, and then ask if the sun rises over a certain village first...

[33724]

how would you know if he were lying?

p.s. you have no items

[Waser Lave]

Spoiler! --Click here to view--

Ask if he's a woman?

[Sweeney]

"Which way would a member of the other tribe tell me to go, in order to reach the village

(And then take the other route.)

[phalkon]

i'd agree with joe on this, but as far as directions go, most common folks know which direction the sun rises from. so if the dude's like "oh, the sun rises in this direction" go the opposite way.

but like i said, joe made it simpler

[The Dirty Filipino]

One Sunday evening after working in the fields, the secluded monks of the Kaetorsian order gathered for evening prayers. After the usual somber songs and pious prayers, the high priest said, “I have a grave announcement. It appears a horrible disease has fallen on our community this fine spring day. Some of you have acquired a disease from working in the fields today. I know this because the disease results in a purple spot on your forehead, and I can see that some of you have this. From what I know of this most evil disease - you will remain unharmed for 14 days. After which, the disease will spread to others, and you will experience a most painful passing that may last months. If we are not careful, this disease will completely destroy our peaceful monastery. Therefore, I ask that those of you who have this spot please remove yourself from our community before these two weeks are over. Despite the fact that all of you have taken a vow of silence, and a vow of humility, and thus will not be able to inform one another of the forehead spot, and even though we lack mirrors and the lake is choppy and you are unable to see for yourself whether you have this spot, you are all trained highly in the ways of logic and will be able to deduce on your own whether or not you have become infected. In this way, we will carry on as we always have. You will work in solitarily all morning and we will congregate here every evening to welcome one another to this holy life we share. Some of you would prefer that I simply point out those of you who are diseased and while I have not taken the vow of silence that you have taken, my vow of humility prevents me from calling attention to your dysfunctions. Good night”
The next few days passed as they always have. The monks that had been infected seemed as good natured as the others, and no one treated one another any differently. However, after more than a week, as the two week deadline approached, an air of nervousness crept in. The second Saturday after the high priest’s announcement was particularly tense. The next day marked the two week deadline before the disease was to spread again, and the diseased monks were still working and praying along side the healthy ones. After the congregation disbanded from the Saturday evening prayers, the monks returned to their private quarters. On Sunday, two weeks after the high priest announcement, all of the diseased monks were gone. Through their highly tuned logic skills, they were able to determine that they had been affected and removed themselves.
How many monks were infected? And how did they determine it?

[Daniel#1]

Spoiler! --Click here to view--

Ok let's see, ask him, "If I asked the other tribe member, what road would he take, would he say the right or left" You then take the other road.

well that was quicker than expected.

could you use spoiler []'s nextime.




A logician vacationing in the South Seas finds himself on an island inhabited by two tribes. One of liars, and one of truth-tellers. Members of one tribe always tell the truth and members of the other tribe always tell lies. he comes to a fork in the road and has to ask a native bystander which branch he should take to reach a village. he has no way of telling if the native is a truth-teller or a liar. The logician thinks for a moment, then asks one question only. From the reply he knows which road to take. What question does he ask?

Spoiler! --Click here to view--

Ok let's see, ask him, "If I asked the other tribe member, what road would he take, would he say the right (or left)" You then take the other road.

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

• it could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
• What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
• Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
• Random will answer 'da' or 'ja' when asked any yes-no question.^{http://en.wikipedia....e_note-boolos-0}

[phalkon]

this is just like the brown-eyed vs. blue-eyed puzzle posted a while back.

in which case there were many "answers" to that too