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Who stole the Perplexicon? (Posted on 2012-01-11) Difficulty: 3 of 5
An ancient book known as the Perplexicon was stolen from the Limitless Enigmatic Vault of Innovative Knowledge yesterday. When security made their rounds at 6:00pm, they noticed it was missing and went on lock-down. The museum's security tapes for 5:00pm-6:00pm yesterday are missing. Police pulled in suspects for questioning, and each claimed to have an alibi:

Charlie: "I was attending a convention."
Gamer: "I was at the movies."
brianjn: "I was bowling with my friends."

Since police could not determine who were knights, liars, or knaves, let alone who was the thief, they called in the renowned detective Dustin to question them. While the other investigators listened from the next room behind a two-way mirror, the following took place in the interrogation room:

Dustin: "On the night in question, Gamer, you were NOT at the movie theater. You were, in fact, stealing the Perplexicon!"
Charlie: "If Gamer is guilty, then I'm a Martian."
Dustin: "And you, Charlie, claimed you were at a convention."
Charlie: "That is true."
Dustin: "And yet, an eyewitness claims to have seen you fleeing LEVIK at 5:15pm!"
Charlie: "I already said I was at a convention."
Dustin: brianjn, you're being awfully quiet. Your alibi doesn't check out either."
brianjn: "Just because a person's alibi doesn't check out doesn't mean they are guilty. Besides, I really was bowling."
Charlie: In fact, brianjn invited me to join his bowling group, but I had to decline."
Dustin: "Hey, I'm the investigator! I'll ask the questions! Someone in this room is guilty."
Charlie: "It is not I."
brianjn: "It is not I."
Gamer: It is not I."

Who stole the Perplexicon?

  Submitted by Dustin    
Rating: 5.0000 (3 votes)
Solution: (Hide)
I will use the notation C3 to mean Charlie's third statement, and GA to mean Gamer's alibi statement.

First organize everyone's statements:

CA: "I was at a convention."
GA: "I was at the movies."
bA: "I was bowling."

C1: "If G is guilty, then I'm a Martian."
C2: "That (C claimed to be at a convention) is true."
C3: "I said I was at a convention."
C4: "brianjn invited me to bowling."
C5: "I am innocent."

b1: "Person's alibi doesn't check out =/= they are guilty."
b2: "I was bowling."
b3: "I am innocent."

G1: "I am innocent."

Since Charlie stated he was at a convention, his statement C3 "I said I was at a convention" is true. This means C1 and C5 must be true also (whether he's a knave or a knight). By C5, we know Charlie is innocent. Next, let's look at Dustin's statements.

D1: "GA is false."
D2: "G is guilty."
D3: "C made statement CA."
D4: "C is guilty."
D5: "b is being quiet."
D6: "bA is false."
D7: "D is the investigator."
D8: "D will ask questions."
D9: "Someone in this room is guilty."

Since we have already demonstrated that Charlie is innocent, D4 is false. Therefore, D2 is false, and Gamer is innocent. Charlie did claim to be at a convention, so D3 is true. Therefore, Dustin is a Knave where even-numbered statements are false and odd-numbered statements are true.

Since we know D1 is true, then Gamer's alibi must be false, even though he is not the thief. Next, brianjn's first statement says "Just because a person's alibi doesn't check out doesn't mean they are guilty." This means b1 is true, and therefore, b3. So we know brianjn is innocent.

Well then, who stole the Perplexicon?

By D9, we know someone in the room is guilty. Since Charlie, Gamer, and brianjn are innocent, the only other person in the room, Dustin, must be guilty.

Charlie: Knight, innocent.
Gamer: Knave, innocent.
brianjn: Knight, innocent.
Dustin: Knave, guilty.

Interestingly, we still don't know whether Charlie is a Martian or not. Since "If Gamer is guilty" is false, "then I'm a Martian" could be true or false, and the entire statement would still be considered true.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): a solutionDustin2012-01-15 05:16:56
Some Thoughtsre(2): a solutionDej Mar2012-01-15 02:02:55
Hints/Tipsre: a solutionDustin2012-01-14 16:48:34
Some Thoughtsa solutionDej Mar2012-01-12 08:26:03
Hints/TipsKeep going!Dustin2012-01-11 20:16:03
SolutionFun solutionMath Man2012-01-11 18:00:34
solution/spoilerxdog2012-01-11 15:36:03
Some ThoughtsPossible solutionbroll2012-01-11 11:37:51
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