Question

You are in a land inhabited by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a local resident there, but he has time only to reply to one yes-or-no question. What one question should you ask so as to learn which fork to take? Suggestion: Make a table.

Answer 1

SOLUTION:

To negate the falsehood in the liar's reply we may try to either double his lie. Or we will compose a question such that the liar will again forced to say the truth.

A composition of two statements can be as follows: “Is it true that you always say the truth and the right road leads to the capital or you always says a falsehood and the left road leads to the capital?” Here we compose two different statements: A =”you always say the truth” and B =”the right road leads to the capital”. Here is the truth table (NOT what they would report, except for the last column) for both statements and their composition in each case:

Table:

The case	A	B	C=(A∧B)	D=((¬A)∧(¬B))	(C∨D)	Report
The right road leads to the capital
Truth-Teller	T	T	T	F	T	T
Liar	F	T	F	F	F	T
The left road leads to the capital
Truth-Teller	T	F	F	F	F	F
Liar	F	F	F	T	T	F

So, the idea is to simply form a statement that in the case the right roads leads to the capital is true for a truth-teller and false for a liar (so, both would report “Yes”), and vice versa in the case the left road leads to the capital (so, both would report “No”).