Solution to Problem 2.15

1
Solution to Problem 2.15

• ECS 101
• Lab Week 4

2
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 1110 and 1130 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 1010 pm. until
  1230 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 930 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 1000 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?

3
Look at what Jeeves said

• I didn't do it.
• Jessica did it.
• Mr. Legrew was blackmailing Jessica.
• Fifi and I were watching television together from
  1010 pm. until 1230 AM.

• 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.

4
Look at what Jessica said

• 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.

• 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.

5
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.

6
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.

7
Alternative Jessica wasn't being blackmailed.

• Then Jessicas first two statements are true.
• Therefore Jessicas last two statements are
  false.
• Therefore Fifi is innocent (Jessica 4 is F) and
  Julia must be the murderess.
• But if we analyze Julias statements Julia 1, 2,
  3 are False. (An Invalid Argument.)
• This contradicts the fact that each person makes
  two true and two false statements.

8
Therefore Jessica was being blackmailed.

• Then Jessicas second statement is false.
• I was not being blackmailed.
• Fifis third statement is true.
• Jessica was being blackmailed.
• Julia second statement is true.
• Jessica was being blackmailed.

9
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.

10
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.

11
Therefore Jessica wasnt in Chicago.

• Then Jessicas third statement is false.
• I was in Chicago during the entire night of the
  murder.
• So Jessicas fourth statement must be true.
• Fifi is the murderess.
• And the Problem is solved.

12
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 1010 pm. until 1230
  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).

13
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 1000 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 930 pm. on the night of the murder.
• Julia 4 is False. I saw Jessica leave the house
  at 1000 pm.
• This confirms the solution Fifi dunnit.