A very unconventional solution to the world’s most difficult logic puzzle

[Santa-Klaus]

I came across this puzzle a few days ago, it’s supposedly the most difficult logic puzzle in the world, made by a Harvard professor of psychology. I was unable to solve it (after several hours of scratching my head) and eventually had to concede defeat.

I did however come across a very unconventional solution to the puzzle that is acceptable based on the criteria stipulated by the creator of the puzzle, as far as I can tell that is (not the Wikipedia solution). I am however unsure whether others will agree with this assertion or not.

“Three gods A, B, and C are called, in no particular 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”

[harey]

I do not really fancy this kind of problem. The solution usually is "What would answer the god B if the god A asked him what would answer the god C if..."

Did you think about something like that?

[phil1882]

how would God A answer God B to the question is da yes?

then ask how would God C answer God B to the question is da yes?

or something similar.

Edited March 31, 2014 by phil1882

[joef1000]

Suppose we knew for sure that the god we are talking to is NOT the random god. Then, if we ask

"If I asked you X, would you say da?"

There are 8 possibilities:

1) X is no, da means no, you are talking to the truth god.

If you asked him X, he'd say no, which is da, so the answer to the question you asked him is yes, so he says ja.

2) X is no, da means no, you are talking to the false god

If you asked him X, he'd lie and say yes, which is ja, which he'd lie about and say yes, he would say da, so he'd say ja (yes)

3) X is no, da means yes, you are talking to the true god

If you asked X, he'd say ja (no), so he'd tell you that no, he wouldn't say da(y, so he'd say ja (no)

4) X is no, da means yes, you are talking to the false god

If you asked X, he'd lie and say da (yes), so he'd lie about saying da and say ja (no)

5) X is yes, da is no, you are talking to true

If you asked X, he'd say ja (yes), so he'd say that no (da), he wouldn't say da.

6) X is yes, da is no, you are talking to false

If you ask X, he'd lie and say da (no), so he'd lie and say no (da) that he won't say da.

7) X is yes, da is yes, you are talking to true

If you ask X, he would say da (yes), so he would say da so the answer is yes (da)

8) X is yes, da is yes, you are talking to false

If you ask X, he would lie and say ja (no), so he'd lie about that and say yes (da) that he would say da.

So, when you ask "If I asked you X, would you say da?", then you can interpret da as yes regardless of what it actually means and who you are talking to as long as it's not the random god.

So, how do we know whether we are talking to the random god or not?

The obvious way is to ask someone.

So if we asked A "Is B random?" (in the form we could derive a meaningful answer from - "If I asked you if B was random, would you say da?") there are 3 possibilities:

A is random, B is random, or C is random.

Let's analyse these:

1) If A is random, it doesn't matter what he says, because whichever of the other 2 you go to can't be random.

2) If B is random, A will tell you da, you can go to C

3) If C is random, A will tell you ja, you can go to B

So, you can go to B if A says ja, and C if he says da, even if it turns out A is random.

You can then use whoever you want to to determine the identity of all 3 in 2 questions (are you true, is A random, (obviously both stated in the da-means-yes-no-matter-what form above))

3 questions total.

BTW; I have seen this question before and I'm not some kind of super genius who just worked out that answer in 5 minutes.

Edited April 5, 2014 by joef1000