1

Suppose a certain country is inhabited by truth teller and liars, who only respond to yes or no questions. A tourist comes to a fork in the road where one branch leads to the capital, and the other does not. There is a native standing at the fork. What yes or no question should the tourist ask to determine which branch to take?

The tourist can ask "If I were to ask you if the left branch leads to the capital, would you say yes?" By construction, if Yes, then left branch leads to the capital. If No, then it doesn't.

My book however, suggests letting $A$ be "you are a truth teller" and $B$ be "the left branch leads to the capital." Construct a formula from $A$ and $B$, call it $F$, so when asked "Is the statement F true, the native replies yes iff $B$ is true.

How can we construct $F$?

Bruno Bentzen
  • 3,362
user232751
  • 99

2 Answers2

1

"If I ask the other kind of person, whether the right road leads to the capital , he will say YES, won't he? "

Explanation: ((( Assuming left road is the correct Path ... ))) Liar will say "Yes" Truth teller -"Yes"

Liar knows that truth teller knows the truth and will say no when asked So liar will tell the opposite which is "yes". Truth teller knows that the liar will lie and will say yes about right road being correct, So truth teller will also say "Yes" indicating that the liar will say yes.

So I will take the other road.

gproxy
  • 11
-1

I think you're supposed to ask: "If you were a truth teller, would you tell me if the left branch leads to the capital?". If the native is a truth teller, he will confirm that he would say yes if the left branch does indeed lead to the capital. If the native is a liar (and the left branch does lead to the capital), he would tell you that the left branch doesn't lead to the capital. However, he would ALSO lie to you when you ask him the question above. He would lie about lying, so his answer would have to be "yes" as well.

panonski
  • 124