The Fork

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With a tip of the hat to itsmeee's 999 puzzle, and bonanvoa's Mad Hatter puzzle...

You come to a three-way fork in the road. You know that one path leads to your destination, and that the other two paths lead to Certain Doom. You know that in the area is a tribe of truth-tellers and a tribe of liars, both of which will answer appropriately whenever they can, or remain silent whenever they cannot answer a question truthfully (or falsely). A tribesman from one of these tribes -- you know not which -- is standing at the fork, and -- as if for his own amusement -- offers to answer one single question with "Yes" or "No" to help you find your way. What question do you ask him?

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Posted · Report post

Should we take into account that his offer is not to be taken as reliable in the case that he is a liar?

Or should we assume a trusted person tells us this person will truthfully or falsely answer a yes/no question if possible?

I assume it's the latter, but the former would be interesting to analyze as well.

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Posted · Report post

Ask which way would a member of the other tribe tell you is the correct path to your destination. Then go the other way.

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Posted (edited) · Report post

Should we take into account that his offer is not to be taken as reliable in the case that he is a liar?

Or should we assume a trusted person tells us this person will truthfully or falsely answer a yes/no question if possible?

I assume it's the latter, but the former would be interesting to analyze as well.

I was thinking the latter... but since you mention it, let's analyze. :) Do any possible "false offers" from a lying tribesman result in a different approach? The only ways I can think for the offer itself to be a lie is if he will answer more than just one question (which only makes life easier), or will not answer any questions (which means you just have to guess), or will choose his answer from some other set of responses besides "Yes / No" (which I think would leave you with too little information to ask the right question). Any other options I missed?

Edited by ThunderCloud
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Posted · Report post

Ask which way would a member of the other tribe tell you is the correct path to your destination. Then go the other way.

This will work for some similar puzzles, but not this one. :) The tribesman will answer one question with "Yes" or with "No", and that is all. He will not point to the correct path. Furthermore, as this is a three-way fork, there is still a choice of two "other ways" you can go even if you eliminate one option.

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Posted · Report post

Should we take into account that his offer is not to be taken as reliable in the case that he is a liar?

Or should we assume a trusted person tells us this person will truthfully or falsely answer a yes/no question if possible?

I assume it's the latter, but the former would be interesting to analyze as well.

I was thinking the latter... but since you mention it, let's analyze. :) Do any possible "false offers" from a lying tribesman result in a different approach? The only ways I can think for the offer itself to be a lie is if he will answer more than just one question (which only makes life easier), or will not answer any questions (which means you just have to guess), or will choose his answer from some other set of responses besides "Yes / No" (which I think would leave you with too little information to ask the right question). Any other options I missed?

I would add to the list:

  1. Answer a different number of questions
  2. Or none at all
  3. Replies other than yes/no
  4. promise that his yes/no answer would be truthful may not be reliable.

It was option 4 actually that came to my mind.

But perhaps a liar lying about telling the truth and having to tell the truth for the false promise to be false cancels out.

e.g. Both a T and a L will say "I am telling the truth;" neither can say "I am lying."

It's probably the latter, and we are worrying about nothing.

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Posted · Report post

I was thinking the latter... but since you mention it, let's analyze. :) Do any possible "false offers" from a lying tribesman result in a different approach? The only ways I can think for the offer itself to be a lie is if he will answer more than just one question (which only makes life easier), or will not answer any questions (which means you just have to guess), or will choose his answer from some other set of responses besides "Yes / No" (which I think would leave you with too little information to ask the right question). Any other options I missed?

I would add to the list:

  1. Answer a different number of questions
  2. Or none at all
  3. Replies other than yes/no
  4. promise that his yes/no answer would be truthful may not be reliable.

It was option 4 actually that came to my mind.

But perhaps a liar lying about telling the truth and having to tell the truth for the false promise to be false cancels out.

e.g. Both a T and a L will say "I am telling the truth;" neither can say "I am lying."

It's probably the latter, and we are worrying about nothing.

I'd tend to agree; the liar and truth teller will both claim to offer honest assistance. The liar instead offers dishonest assistance by lying in response to the question, thus making his original offer a lie, and preserving his "alignment" as a liar.

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