Kachana

From the Harvard Review of Philosophy, 1996.

Three Gods, A B and C, are called, in some order, True False and Random. True always speaks truly, Flase 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 exacltly 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.

Som clarifications:

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 though of as depending on the flip of a coin: heads = true, tails = false.

Random will answer da or ja when asked any yes-no question.

[ March 22, 2002: Message edited by: Kachana ]</p>

Laera

Does this even have a solution? It seems as though it would take at least two questions to determine any one of them, but one question wouldn't be enough to tell the difference between the other two if "Random" doesn't pan out right.

Has anyone ever solved this?

Malaclypse the Younger

Problems of this type are usually solved by asking questions to one god that refers to the another (it is presumed that each of the gods knows the identities of the others).

For instance, one might ask of god A, "Is God B a liar?" or "Would God B answer ja if asked he was a 'False'?"

[ March 22, 2002: Message edited by: Malaclypse the Younger ]</p>

Kachana

It does have a solution, I think there are more than one solutions. The paper I got it from was actually presenting a simpler solution than the simplest that has been presented thus far. I gave up after about 5 minutes through fear for my sanity.

John Page

I think it must be a misprint, there are no gods. Perhaps they meant dogs, please confirm.

A second clarification please, you specify "The gods understand English, but will answer all questions in their own language...." do the dogs all speak different languages than each other?

Cheers!

Kachana

Well, if you asked False if there are any Gods, he's say no (in his own language of course), but in this instance he is telling the truth. The plot thickens.

They all speak the same language, but I'll give you a hint, determining which of 'da' and 'ja' means 'yes' and 'no' is not necessary.

Bill Snedden

This puzzle is horribly, horribly difficult. <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />

Kachana, you should be scourged for posting it. It will certainly cause much loss of productive time this evening or tomorrow (good thing it's the weekend!).

I think I know the answer, but I'm going to refrain from posting because I had a couple of hints.

I'll provide those to everyone else, just to be fair :

1) Determining which means "yes" or "no" isn't important, but the solution is determined based upon an assumption.

2) The questions asked are complex, rather than simple.

This should make your brain hurt. It did mine...

Bill

jupstin

I have a clarification question:

you said:

Can I at least assume that gods A, B, and C will have the same word for '"yes" and "no?" Please don't tell me that "da" means "yes" for A and "no" for B...

Kachana

Don't worry, these God's are consistent in their use of 'da' and 'ja', even though they have glaring inconsistencies in their attributes of benevolence, omnipotence, and omniscience.

Malaclypse the Younger

What I'm curious to know is if this sort of problem has a general algorithmic or algebraic solution.