1. If Brian is the truthteller . . . If John is the truthteller . . .
Detective Problem
Detectives have four suspects in a case. Suppose the detectives know that of the four suspects, exactly one person is telling the TRUTH.
If then statement: If exactly one person is telling the truth, then exactly three people are lying.
Original Statements
If Brian is the truthteller . . .
If John is the truthteller . . .
If Carlos is the truthteller . . .
If Diane is the truthteller . . .
Brian: Carlos did it.
John: I did not do it.
Carlos: Diane did it.
Diane: Carlos lied when he said that I did it.
Any contradictions?
Carlos did not do it.
Carlos did not do it.
Carlos did not do it.
Carlos did it.
I (John) did it.
I (John) did not do it.
I (John) did it.
I (John) did it.
Diane did not do it.
Diane did not do it.
Diane did not do it.
Diane did it.
Carlos told the truth when he said that I (Diane) did it.
Carlos told the truth when he said that I (Diane) did it.
Carlos told the truth when he said that I (Diane) did it.
Carlos lied when he said that I (Diane) did it.
YES
YES
YES NO

2. Diane: Carlos lied when he said that I did it.
Detective Problem #2
Detectives have four suspects in a case. Suppose the detectives know that of the four suspects, exactly one person is LYING.
If then statement: If exactly one person is lying, then exactly three people are telling the truth.
Original Statements
If Brian is the liar. . .
If John is the liar. . .
If Carlos is the liar. . .
If Diane is the liar. . .
Brian: Carlos did it.
John: I did not do it.
Carlos: Diane did it.
Diane: Carlos lied when he said that I did it.
Any contradictions?
Carlos did not do it.
Carlos did it.
Carlos did it.
Carlos did it.
I (John) did not do it.
I (John) did not do it.
I (John) did it.
I (John) did not do it.
Diane did it.
Diane did it.
Diane did it.
Diane did not do it.
Carlos lied when he said that I (Diane) did it.
Carlos lied when he said that I (Diane) did it.
Carlos lied when he said that I (Diane) did it.
Carlos told the truth when he said that I (Diane) did it.
YES
YES NO
YES