Pick the right door

[BMAD]

Inspired by a couple of puzzles written by Bonanova and I believe TSLF a few months ago:

Three guards stand by three doors in an unknown order. The three doors lead to Hell, Heaven, and Limbo; the three guards follow the standard rituals that these problems tend to follow; that is, one always tells the truth, one always lies, and one responds with a random response. The guards understand English (and other languages for that matter), but will only speak a two-word language in which Ja and Da mean 'yes' and 'no,' but you do not know which means which. The Random's mind can be modeled as a fair coin flip for which, if it lands heads, he will say Ja; if tails, Da. You can ask up to three yes-no questions total. If faced with a question that cannot be answered, the guards will simply ignore your question (and you lose your question). Which three questions should you ask to determine which door leads to Heaven (you do not need to determine any other information).

[Yoruichi-san]

I'm going to call the guards A,B, and C, and the doors 1,2, and 3 for the sake of clarity:

Ask A, "If I ask you if B is the random answerer, would you say ja?" If he says ja, then either A or B is Random. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

.

[BMAD]

I'm going to call the guards A,B, and C, and the doors 1,2, and 3 for the sake of clarity:

Ask A, "If I ask you if B is the random answerer, would you say ja?" If he says ja, then either A or B is Random. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

.

hmmm, are you assuming you know what Ja and Da means?

on:

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

if the guy you ask is a liar, won't your conclusion be wrong?

[Yoruichi-san]

I'm going to call the guards A,B, and C, and the doors 1,2, and 3 for the sake of clarity:

Ask A, "If I ask you if B is the random answerer, would you say ja?" If he says ja, then either A or B is Random. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

.

hmmm, are you assuming you know what Ja and Da means?

on:

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

if the guy you ask is a liar, won't your conclusion be wrong?

It's running the question through him twice, i.e. "what would you say if I ask you" rather than directly asking him, so if he lies, the lies make a double negative.

It's probably the most common strategy in these kind of puzzles . I can see how the phrasing might be confusing in this context, so if you like, you can rephrase the question "If I ask you on the next question 'is door 1 the door to heaven', would you say ja?"

[BMAD]

I'm going to call the guards A,B, and C, and the doors 1,2, and 3 for the sake of clarity:

Ask A, "If I ask you if B is the random answerer, would you say ja?" If he says ja, then either A or B is Random. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

.

hmmm, are you assuming you know what Ja and Da means?

on:

Ask the one you know is not the random god, "If I ask you if 1 is the door to Heaven , would you say ja?", if he says ja 1 is the door to heaven, and you're done, if not, ask him the same question about door 2, if he answers ja, it's door 2, if da, it's door 3.

if the guy you ask is a liar, won't your conclusion be wrong?

It's running the question through him twice, i.e. "what would you say if I ask you" rather than directly asking him, so if he lies, the lies make a double negative.

It's probably the most common strategy in these kind of puzzles . I can see how the phrasing might be confusing in this context, so if you like, you can rephrase the question "If I ask you on the next question 'is door 1 the door to heaven', would you say ja?"

does it matter what Ja means?

[Yoruichi-san]

b/c it is again a double negative if it means no...i.e.

If I asked you 'is the sky blue', would you say yes? -yes, if I asked you 'is the sky blue', would you say no? -no

If I asked you 'is the sky red', would you say yes? -no, if I asked you 'is the sky red', would you say no? -yes