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.
If Becky did it then there are 4 liars.
If Betty did it then there is only 1 liar.
If neither did it then there are 2 liars.
So the only valid values for k are 1, 2 and 4.
In cases 1 and 4 we know there are not exactly 2 liars, so one of the two did it, and by similar reasoning determine which is was (4 liars means there were not exactly 1 liar, and vice versa, so that the contrapositives work).
If k=2 neither Becky nor Betty did it, by similar reasoning, but who did it?
It couldn't be Bernie, as he told the truth.
It could be Benny, since he lied.
It couldn't be Bella, as she told the truth.
So in fact if k=2 it must be Benny.

Posted by Charlie
on 20160620 18:46:16 