# The Hardes Logic Puzzle Ever!

tomtom232
Posers and Puzzles 04 Oct '11 20:14
1. 04 Oct '11 20:14
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 two 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
-What the second question is, and to which god it is put, may depend on the answer to the first question.
-Whether Random speaks da or ja should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks da; if tails, ja.
2. 05 Oct '11 14:20
Originally posted by tomtom232
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
You mean Da and Bal.

HTH; HAND.

Richard
3. 05 Oct '11 16:05
Originally posted by Shallow Blue
You mean Da and Bal.

HTH; HAND.

Richard
No thats the zombies and knaives on the island logic poser... this one is different.
4. 12 Oct '11 07:392 edits
There seem insufficient questions to me.

There are 6 permutations:
TLA
TAL
LTA
LAT
ATL
ALT

With the first question we are going to get da or ba

This can only split the 6 combinations into 2 3s.

But with only one more question we can only split each 3 into a 1 and a 2, so we need to get lucky, we can't guarantee knowing what they are in 2.

If the puzzle was to find the location of T in two questions, we might be able to do that.
5. talzamir
Art, not a Toil
12 Oct '11 11:08
I agree. Given that you don't know what the words mean and you don't know what mood Random is for the first question, or the second question, there are plenty of permutations. Six different arrangements, or 12 after taking into account that random's answers can be true or false, or 24 given after taking into account that the answer can mean one thing or the opposite. That with just two orders.. well, it feels to me I would need to be one of the three gods to pull that off.
6. 12 Oct '11 19:211 edit
Glad you agree Tal. Perhaps it can be done in 3 questions, but two is definitely not enough.
7. 12 Oct '11 21:432 edits
Two is enough.

disclaimer: only read hint if you want to make the problem very easy for yourself.

da and ba are not the only possible answers
8. 13 Oct '11 07:35
Hmm, You do say they have to be "yes-no" questions..
9. talzamir
Art, not a Toil
13 Oct '11 10:16
It will be fascinating to learn the answer to this one. Unless one accepts
questions of multiple parts like, from right to left, what would each of you say if I ask &#039;do you sometimes lie, sometimes tell the truth
or
yes-no questions where silence is effectively a third answer
then for now I'm currently unable to proceed. I wonder what randomness here is.. the gods know which is which? Do they know when random lies / will lie?
10. 13 Oct '11 16:301 edit
Random doesn't speak true or false but randomly answers da or ja. Yes, multiconditional questions are acceptable as long as they are one complete yes-no question.
11. 14 Oct '11 19:52
Big hint since nobody is attempting this.

Would you answer ja to the question of whether you would answer da to this question?

Niether true nor false can answer this question so silence (or an exploding head ðŸ™‚ ) must be acceptable.
12. uzless
The So Fist
19 Oct '11 19:05
1 Ask one of the gods this:

Would you answer ja to the question of whether you would answer da to this question?

Niether true nor false can answer this question so silence (or an exploding head ) must be acceptable. If the god answers you know it's random god and can exclude him.

2A Ask one of the other gods this:

"If i asked the other god if he was the liar, what would he say?"

If he answers, NO, then he is the truth teller, if he answers yes, he is the liar

2B if the first god is silent, then you know he isn't random so,

Ask the same god the following while pointing to another god:

"If i asked the other god if he was the liar, what would he say?"

If the god you are asking is the truth teller, and the god you point to is the liar he will say "no" If the god you point to is random, he won't be able to answer.

If the god you asking is the liar, and the god you point to is the truth teller, the liar will say "YES" If the god you point to is random, he won't be able to answer.

13. 21 Oct '11 00:48
Originally posted by uzless
1 Ask one of the gods this:

Would you answer ja to the question of whether you would answer da to this question?

Niether true nor false can answer this question so silence (or an exploding head ) must be acceptable. If the god answers you know it's random god and can exclude him.

2A Ask one of the other gods this:

"If i asked the other god if ...[text shortened]... "YES" If the god you point to is random, he won't be able to answer.

If the god you are asking is the truth teller, and the god you point to is the liar he will say "no" If the god you point to is random, he won't be able to answer.

If the god you asking is the liar, and the god you point to is the truth teller, the liar will say "YES" If the god you point to is random, he won't be able to answer.

Thus, your proposed solution fails. If you get silence on your first proposed question; and then get silence on your second proposed question; then you have failed the task.
14. talzamir
Art, not a Toil
22 Oct '11 17:40
Even with the helpful clue I have trouble with this. Far as I can tell, as long as you don't know whether you're talking with random or not you can't get useful answers. Hence the question,

To God A: "What will Random say when I ask, 'are you Random'?"

Random says "ja" or "da", I don't really care which. True and Lie say nothing as they have no clue what Random will say.

If A says nothing, I know that A is Random.

"is the answer to 'does da mean yes' the same as the answer to "is A Random?"

True answers "da", Lie answers "ja", so the second question settles everything, so two questions suffice.

However, if the first answer is silence, all that is learned is that A is not random.

So the possibilities remain

True - Random - Lie
True - Lie - Random
Lie - Random - True
Lie - True - Random

the second question can cover three possibilities.. a yes answer, no answer, or silence. But out of four possibilities, is that enough?