Mr. Smith was murdered in Kansas City. The police determined that the time of death was between 11:10 pm and 11:30 pm. Four suspects were questioned: Butler, the butler; Cook, the cook; Ruby, the maid; and Irma, Mr. Smith’s secretary.

The suspects made the following statements:
Butler: I did not do it. Irma did it. Mr. Smith was blackmailing Irma. Ruby and I were watching television together from 10:10 p.m. until 12:30 a.m.
Cook: I am innocent. Irma was being blackmailed. Butler murdered Mr. Smith. I saw Irma leave the house at 10:00 p.m.
Ruby: I am innocent. Butler and I were watching television together at the time of the murder. Irma was being blackmailed. I saw Irma speaking to Mr. Smith at 9:30 p.m. on the night of the murder.
Irma: I did not kill Mr. Smith. I was not being blackmailed. I was in St. Louis during the entire night of the murder. Ruby is the murderess.

If each suspect made exactly two true statements and told exactly two lies, determine who killed Mr. Smith.

This solution is based upon the added premise that there was only one killer.  If the possibility that two people could have killed Smith is accepted, all bets are off.
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Neither Butler nor Irma did it because their statements include a denial, an alibi, and an accusation,
meaning that if their denials were untrue, so would be their accusations and alibis,
giving them three false statements.

Of Butler's two remaining statements (Irma blackmailed and Butler/Ruby alibi), one is true and one is false. 
And Ruby shares these statements.

Ruby and Irma conflict on three statements (Irma blackmailed, Ruby did it, and Irma's St. Louis alibi). 
For Irma, one is true and two false, while for Ruby, one is false and two true. 
Which makes Ruby's fourth statement (the Butler/Ruby alibi) false.

Thus, Irma was blackmailed.

If Irma was in St. Louis, then Cook's denial becomes true AND Ruby's denial also becomes true.  Thus, Irma couldn't have been in St. Louis.

Conclusion:  Ruby did it.  And Cook lied about seeing Irma in KC at 10:00.

Posted by hoodat on 2017-03-11 23:27:04