In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie.
You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it.
Upon asking, the person replies the following:
“The result of the toss is head if and only if I am telling the truth.”
How do I understand that the result is Head. No matter who speaks those words.
Not able to grasp it. Although, it is clear that if these words are from truth-teller then definitely the result is Head. But what if it was the Liar who said them?
Best Answer
$X={}$“The result of the toss is head if and only if I am telling the truth.” $$ \begin{array}{|c|c|c|} \hline \text{type of person} & \text{coin outcome} & \text{Could say $X$?} \\ \hline \text{truth-teller} & \text{head} & \text{yes} \\ \text{truth-teller} & \text{tail} & \text{no} \\ \text{liar} & \text{head} & \text{yes} \\ \text{liar} & \text{tail} & \text{no} \\ \hline \end{array} $$ The third column is "yes" when the outcome is a "head"; otherwise it's "no".