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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?

See The Solution Submitted by Dustin    
Rating: 5.0000 (3 votes)

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Some Thoughts a solution | Comment 5 of 8 |

Assuming each individual is a Knight, Knave or Liar....
As Charlie's sequential responses to Dustin's confirmation seeking statements to Charlie's alibi ("That is true" and "I already said I was at a convention") can be paraphrased to be the same statement, either both are true or both are false. Either way Charlie can not be a Knave, as they do not alternate between truth and fallacy (by definition of a Knave).

Since the alleged eyewitness claimed to have seen Charlie leaving the LEVIK, either Charlie's claim at attending a convention at the time is a lie, the eyewitness lied, or Dustin lied about there being an eyewitness.
If Charlie is a Liar, then, from the material conditional and his claim of not being guilty, both he and Gamer are guilty, which could be interpreted as a convention with both involved in the heist of the Perplexicon. Thus Charlie could not be a Liar, and either the eyewitness was either a Liar or a Knave, or there was no eyewitness and Dustin, himself, is a Liar or a Knave.

From brianjn's sequence of statements, as brianjn stated "Just because a person's alibi doesn't check out doesn't mean they are guilty", which is a true statement, either he, himself, is a Knave who gave a false alibi or he is a Knight.

Given Charlie as a Knight who did not steal the Perplexicon, his statement that brianjn invited him to go bowling supports brianjn's alibi. Therefore (assuming the invitation wasn't a clever premeditated pre-planned cover-up), brianjn must be a Knight, and did not steal the Perplexicon.

Assuming, then, Charlie is not a Martian, from the material conditional statement, Gamer is also not guilty and is either a Knave with no alibi or he is a Knight who went to the movies. This would mean the renowned detective Dustin was a Knave.

By deduction from Dustin the Knave's statements, Gamer is a Knave who gave a false alibi and brianjn is a Knight. And from the final statement by Dustin that someone in the room was guilty, and as Charlie, Gamer and brianjn are innocent, Dustin himself effectively admitted to the theft.

Thus, either Charlie is a Martian with no conclusion yet reached as to the guilty party and/or brianjn had extreme foresight in pre-meditated planning, OR Dustin is the thief.  

  Posted by Dej Mar on 2012-01-12 08:26:03
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