Three suspects are arrested for a bank robbery. Suspect $A$ says he did not rob the bank. Suspect $B$ says he did not rob the bank. Suspect $C$ says suspect $B$ did not rob the bank.
If $A$ is telling the truth, then that means $B$ and $C$ are lying, which means that $B$ robbed the bank.
Is this correct?
EDIT: Sorry for not including this, the restriction is only one is telling the truth.
On
Assume A is telling the truth, then B and C must be lying then, B must rob the bank, but as B is lying, he must have robbed the bank, C is lying so B has robbed the bank, So A is not lying, he's telling the truth.
Assume B is telling the truth then A and C are lying, then B must rob the bank according to C, contradiction.
Assume C is telling the truth so B hasn't robbed the bank, B is lying this means he has robbed, contradiction.
Given the assumption that only one suspect is telling the truth, the solution can be established in one fell swoop: If B is telling the truth, then C is also telling the truth; this would violate the assumption, so B must be lying, and hence he is the robber.
You can, of course, consider all the other possibilities as well and rule them all out, but you don't need to.