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 Find the killer (Posted on 2016-06-20)
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.

 See The Solution Submitted by Ady TZIDON Rating: 5.0000 (1 votes)

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 K is for killer (spoiler) | Comment 1 of 5
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.

 Posted by Steve Herman on 2016-06-20 16:06:30

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