Solution to Problem 2.15 ECS 101 Lab Week 4 Problem 2.15 On Wednesday, May 5, 1976, the wicked Simon Legrew was murdered at his home in a Boston suburb. The police were able to place the time of death at between 11:10 and 11:30 pm. They arrested four suspects - Jeeves, the butler; Fifi, the French maid; Julia, the cook; and Jessica, Mr. Legrew's private secretary. Under questioning, the four suspects made the following statements: Jeeves: I didn't do it. Jessica did it. Mr. Legrew was blackmailing Jessica. Fifi and I were watching television together from 10:10 pm. until 12:30 AM. Fifi: I'm innocent. Jeeves and I were watching television together at the time of the murder. Jessica was being blackmailed. I saw Jessica speaking to Mr. Legrew at 9:30 pm. on the night of the murder. Julia: I'm innocent. Jessica was being blackmailed. Jeeves murdered Mr. Legrew. I saw Jessica leave the house at 10:00 pm. Jessica: I did not kill Mr. Legrew. I was not being blackmailed. I was in Chicago during the entire night of the murder. Fifi is the murderess. Each of the four suspects made two true statements and told two lies. Whodunnit? Look at what Jeeves said Our Argument: Jeeves made three statements (1, 2, 4) implying his innocence. At least one of these must be true. Therefore, Jeeves didn't do it. I didn't do it. Jessica did it. Mr. Legrew was blackmailing Jessica. Fifi and I were watching television together from 10:10 pm. until 12:30 AM. Look at what Jessica said Our Argument: Jessica made three statements (1, 3, 4) implying his innocence. At least one of these must be true. Therefore, Jessica didn't do it. I did not kill Mr. Legrew. I was not being blackmailed. I was in Chicago during the entire night of the murder. Fifi is the murderess. Start a Table of True and False Statements Jeeves 1 “I didn't do it.” is True. Jeeves 2 “Jessica did it.” is False. Jessica 1 “I did not kill Mr. Legrew.” is True. Julia 3 “Jeeves murdered Mr. Legrew.” is False. T F F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves Now We Need Alternatives No other answers can be determined from what is given. We need to assume some answers and see if they are correct (Alternatives). Since everyone refers to Jessica's being blackmailed, let's consider the possibilities: She was being blackmailed, or She wasn't being blackmailed. Alternative: Jessica wasn't being blackmailed. Then Jessica’s first two statements are true. Therefore Jessica’s last two statements are false. Therefore Fifi is innocent (Jessica 4 is F) and Julia must be the murderess. But if we analyze Julia’s statements: Julia 1, 2, 3 are False. (An Invalid Argument.) This contradicts the fact that each person makes two true and two false statements. F F T T F F F F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves Therefore Jessica was being blackmailed. Then Jessica’s second statement is false. “I was not being blackmailed.” Fifi’s third statement is true. “Jessica was being blackmailed.” Julia second statement is true. “Jessica was being blackmailed.” F T F T T F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves We have to look at Different Problems and Their Alternatives Again we are stuck. Now we have to make further assumptions. But where? Lets consider two cases of whether or not Jessica was in Chicago. Alternative: Jessica went to Chicago. Then Jessica 1 and 3 are true, Forcing Jessica 4 to be false, So that Fifi is innocent, and Julia is the murderess. But then, Julia 1, 3, and 4 are false, again giving a contradiction. Another Invalid Argument. F T F T F F T F T F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves Therefore Jessica wasn’t in Chicago. Then Jessica’s third statement is false. “I was in Chicago during the entire night of the murder. “ So Jessica’s fourth statement must be true. “Fifi is the murderess.” And the Problem is solved. T F F T F T T F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves Or is it? We should complete the table and make sure it is consistent with our conclusion. Fifi 1 is false. “I'm innocent.“ Jeeves 4 is false.” Fifi and I were watching television together from 10:10 pm. until 12:30 AM. “ Therefore Jeeves 3 is True (2 F and 2 T). Fifi 2 is false. “Jeeves and I were watching television together at the time of the murder.” Therefore Fifi 4 is True (2 F and 2 T). T F F T F T T T F F F T F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves Complete the Analysis and the Chart We know Julia 1 is True. “I'm innocent.“ Thus Julia 4 is False (2 F and 2 T). “I saw Jessica leave the house at 10:00 pm. “ Checking the consistency of the clues determined by 2 F and 2 T: Jeeves 3 is True. “Mr. Legrew was blackmailing Jessica.” Fifi 4 is True. “I saw Jessica speaking to Mr. Legrew at 9:30 pm. on the night of the murder. ” Julia 4 is False. “I saw Jessica leave the house at 10:00 pm. “ This confirms the solution: Fifi dunnit. T F F T F F T T T T F F F T F T 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 Jessica Julia Fifi Jeeves