Forensic Science
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The Liar's Puzzle Solution

Each innocent person had one fact wrong, and the killer lied all the time. Who did it?


Charles and Daisy agree that they all had a long dinner and arrived together. If Charles is the killer, he is lying about this, and Daisy is mistaken. If Daisy is mistaken about this, she must be right that Arnold opened the window. If Arnold opened the window, then Charles must be telling the truth that Betsy didn't open it. But if Charles is telling the truth, he can't be the killer.


If Daisy is the killer, she lied about their having arrived together after the long dinner, and Charles is mistaken there. If Charles is mistaken there, he must be right in everything else. But Charles disagrees with Betsy twice - about whether Betsy opened the window and whether she opened the Scotch. That would make Betsy mistaken twice, and that can't be.


If Betsy is the killer, Charles is mistaken about whether there was gas in the hall, and right about everything else. So when Arnold and Charles disagree about whether the latter turned on the lights, it must be Arnold who is mistaken. Arnold would be right about everything else. But Arnold disagrees with Daisy twice: about what time Arnold said they arrived, and about who pulled poor Eggy out of the oven. If Arnold is right about both, Daisy is wrong twice and that can't be.


So is Arnold the murderer? Yes. Let's take it from top to bottom.

Charles and Daisy are both right about the long dinner and and everybody's arriving together. Arnold lies when he quotes himself as saying they had arrived at seven on the nose - and Daisy is right that he had said six. Charles is also right, however, in claiming that they had arrived at seven (which would need to be true for anyone to have done the crime, according to the police estimate).

Betsy and Charles are both right about the smell of gas in the hall. Daisy had made a mistake.

Arnold lies about Charles' turning on the lights and Charles is right that they were already on. Arnold lies about pulling Eggy out of the oven, and Daisy is right that she did it. Daisy is right that Arnold opened the window; Charles is right that Betsy did not open the window; and in thinking that she did, Betsy is mistaken.

Arnold lies about Betsy's opening up the Scotch; Betsy is right that Arnold opened it; and in thinking that in was Betsy who did it, Charles is mistaken.

Note that although it is NECESSARY to show a logical possibility of Arnold being the killer, it is not SUFFICIENT to simply show this possibility to prove that it was Arnold. To demonstrate that it was truly Arnold, you must show that Arnold could be the killer, and also that the other three could not be.