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**.

3 people (Bernie, Bella, Becky) say Becky did not do it and 1 (Betty) says that she did.

1 or 3 of these 4 people are lying. So we cannot have 0 or 5 liars.

Other possible k:

k = 1. Betty must be lying, so she is the killer.

k = 2. Betty and Benny must be lying, so the killer is not Betty (or Becky). Since the killer must be a liar, it is Benny.

k = 3. Betty and Benny must be telling the truth, but this is a contradiction, so k cannot = 3.

k = 4. Betty must be telling the truth. So Becky is the killer. No contradiction.

In summary, the only possibilities are

k = 1. Betty is the killer.

k = 2. Benny is the killer

k = 4. Becky is the killer.