# The way to Acarien puzzle

You are on a quest to the find the lost kingdom of Acarien. On your way, you end up at a fork in the road. Both paths look exactly the same. At the junction sits a wise man. The wise man will only speak the words “ça” or “ɠa” meaning either yes or no (you don’t know which means which). The wise man will answer any yes-no question truthfully but will only answer one question. What one question can you ask the wise man which from which you will be sure which path leads to Acarien?

• The setup rather strongly implies that we have no common language, so there isn't any question I can usefully ask. Oct 24, 2014 at 10:09
• @PeterTaylor Assume he took a vow of silence, but was interrupted at the last second, so his vow was incomplete. Oct 24, 2014 at 15:33

Question to be asked = "If I ask you if this is the correct path to go, would you say ça" ? 4 possibilities:

ca = yes
path' correctness = yes

ca = yes
path' correctness = no

ca = no
path' correctness = yes

ca = no
path' correctness = no

Hence we see whenever reply is ga the path is incorrect, if the word asked in the question to the wise man was ca .

• +1 but I think my pronounciation of “ça” will it make impossible for the wise man to understand my question and to answer it correctly. I suspect that thinking about how to answer my question will result in some short circuit in his brain and he will explode. Nov 1, 2014 at 12:15
• Well, the question assumes that we know of the fact that the wise man speaks "ca" or "ga".. Some person/event must have told us about this fact. It is up-to us to perfectly master the art of speaking it in the natural accent of the wise man.. Nov 2, 2014 at 12:35

If I asked you "is it left to Acarien?", would you say ça?

The trick is that the this results in the answer ça if the truthful answer to my embedded question is 'yes', and ɠa if the truthful answer to my question is 'no'. Thus you can deduce the correct path easily from the answer.

• "No the left is the left path... Geez... why would he even ask that?" Oct 24, 2014 at 13:15
• @kaine yes I noticed that awkwardness afterwards... maybe I'll edit Oct 24, 2014 at 13:19
• But are you asking about your left, or his left? And which side of the 3-way junction is he sitting on? :-)
– Joe
Oct 24, 2014 at 16:28