British puzzle creator Hubert Phillips invented this genre of puzzle in the 1930s.
I have slightly modified a puzzle attributed to H.P. (a.k.a. Caliban).
One of five people is a murderer.
Here are their statements:
Bernie: Becky didn’t do it.
Benny: Betty did it.
Bella: Becky is innocent.
Betty: Becky did it.
Becky: I did not do it.
Can you identify the killer?
Given k people, including the killer, lied – provide your answers and reasoning for all possible values of k.
I like Charlie's approach. Here is an even shorter version.
If Bernie did it, then he is telling the truth. Contradiction.
If Benny did it, then there are 2 liars.
If Bella did it, then she is telling the truth. Contradiction.
If Betty did it then there is only 1 liar.
If Becky did it then there are 4 liars.
So, there can only be 1, 2 or 4 liars, making the killer Betty, Benny or Becky, respectively.