How to write exactly one of us is telling the truth? (Liars and truthtellers) I have a question regarding a version of the truthtellers and liars puzzle which I haven't seen anywhere before.
I'm stranded on an island and I know that this island has cannibals, but I don't know how to distingush between who are cannibals and who aren't. I run into  three people on the island, A,B,C, and I ask them: "How many of you are truthtellers?" And A responds "flop flip" in his own native language. I then ask what it means, and B then says "It means only one" whereafter C says: "Don't trust B she is lying. Come with me I'm not a cannibal." How do I know what to do?
I want to set this up in a truth table, but I don't know how to formalize "only one of us is a truthteller" into logic. 
 A: If the question is should you come with $C$ or not then the answer is yes, you should. Just split into cases.
Assume $A$ is telling the truth. Then you know $B$ is lying, because if he was telling the truth then you would get that $A$ really told you only $1$ of them is telling the truth (which you assumed is true) which is a contradiction to that both $A$ and $B$ are telling the truth. So $B$ is lying and $A$ actually told you more than $1$ of them is telling the truth (he couldn't say none of them is telling the truth because he is telling the truth himself). So in that case $C$ is telling the truth and he is not a cannibal. 
Now assume $A$ is lying and $B$ is telling the truth. We'll show this case is not even possible. In that case $A$ really told you only $1$ is telling the truth, but this is a lie. As you assumed that $B$ is telling the truth then you get that more than $1$ of them is telling the truth. So $C$ must be telling the truth. But then his words that $B$ is lying are the truth which is a contradiction to that $B$ is telling the truth. So this case isn't possible. 
Finally assume that both $A$ and $B$ are lying. If you assume $C$ is lying then his words that "$B$ is lying" are a lie and $B$ is actually telling the truth. Once again a contradiction. So again $C$ is telling the truth and is not a cannibal. 
So anyway, we can conclude that $B$ is always lying and $C$ is always telling the truth. 
A: "only one of us is a truthteller" = $$(A\land\lnot B\land\lnot C)\lor(\lnot A \land B \land\lnot C)\lor(\lnot A \land\lnot B \land C)$$
Either only A is a truth-teller, or only B, or only C
iff B is a truthteller, than iff A is a truthteller, than "only one of us is a truthteller" = $$B \leftrightarrow (A \leftrightarrow((A\land\lnot B\land\lnot C)\lor(\lnot A \land B \land\lnot C)\lor(\lnot A \land\lnot B \land C)))$$
iff C is a truthteller, B is a liars = $$C \leftrightarrow \lnot B$$
So the truth table is:
$$
\begin{array}{c|c|c|c}
C & B & A & (B \leftrightarrow (A \leftrightarrow((A\land\lnot B\land\lnot C)\lor(\lnot A \land B \land\lnot C)\lor(\lnot A \land\lnot B \land C)))) \land (C \leftrightarrow \lnot B) \\
\hline
0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0\\
0 & 1 & 1 & 0\\
1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 \\
1 & 1 & 0 & 0\\
1 & 1 & 1 & 0
\end{array}
$$
So as you can see, C is a truth-teller, while A can be a thruth-teller or liar.
