Five mathematicians A B C D E are working in the department

Five mathematicians, A, B, C, D, E, are working in the department one Sunday. Mathematician E makes a pot of coffee to see her through the long afternoon of marking midterms. When she returns to the coffee room for her first cup, she discovers that half of the coffee has already been consumed. She knows no one else has been in the department that day, so she questions her four colleagues and receives the following responses: A: “C did it.” B: “Not me.” C: “D did it.” D: “C is lying.” If only one of these four statements is true, and only one of the four people drank the coffee, who is the coffee thief? Justify your answer

Solution

Deduce by elimination

Suppose, A is thief then, A and C are lying but B and D are telling the truth.

Suppose C is the thief. Then A , B and D are telling truth but only one of 4 can be true.

Now let D be thief, then A and D are lying hwereas B and C are telling truth.

If B is thief, then A, B and C are lying. D is telling the truth which satisfies all the criteria.

Answer: B