Monday, January 31, 2011

logic puzzles

So you like logic?  Try these:

The Puzzle of the Hyena's Alias

The Agency for Counter-Terrorism (ACT) has received information that a European terrorist known as "the Hyena" has entered the United States under an assumed name. Unfortunately, ACT has also received conflicting reports of the Hyena's alias, making it hard to track him down, especially since each of the names is a common one. Four informants were questioned and gave the following information about the alias:
  1. John Wilson
  2. James Moore
  3. Denied that the first name was "John". Last name: "Taylor".
  4. Stated that the previous three informants were each right about one name and wrong about the other.
According to the ACT, the fourth informant is the most reliable. Assuming that the fourth informant is correct, what is the Hyena's alias?

The Puzzle of the Masked Men

During a bank robbery, one of the masked robbers shot a bank guard. The police caught all four robbers and interrogated them in an attempt to determine which was the shooter. Each was questioned while attached to a lie detector machine and testified as follows:
  • Alfie: I'm innocent.
  • Benjy: Charlie is guilty.
  • Charlie: Either Alfie or Benjy was the shooter, I'm not sure which.
  • Denny: Benjy didn't tell the truth when he said that Charlie did it.
According to the lie detector operator, either all but one of the robbers lied or all but one told the truth―he couldn't tell which―and this was confirmed by subsequent evidence. The police are confused and come to you as a logician for help. Can you determine who shot the bank guard?

The Puzzle of the Dead Presidents

After your first success in helping the police crack a bank robbery (see the Resource below), they turn to you for help with another case: A gang of five men wearing masks of five former presidents have committed a series of armored car robberies.
During one of the crimes, the driver of the armored car was shot and killed by a robber. There are no witnesses to the shooting other than the five criminals involved. The gang was caught while still wearing their masks and have refused to reveal their identities, so the police know them only by the name of the president each impersonated. The police determine that each member of the gang had a specific job: the mastermind, the lookout, the wheelman, the safecracker, and the triggerman. Unfortunately, the police aren't able to figure out which role each "president" played. The police are especially interested in who killed the armored car driver, namely, the triggerman.
The members of the gang were questioned individually while attached to a lie detector, and each criminal made only two statements. Assuming that the lie detector is accurate, each criminal made one true statement and one false statement, but the operator of the detector couldn't tell which was which. As usual, the police are baffled.
  • Kennedy:
    1. Johnson is the mastermind.
    2. Neither Reagan nor Johnson is the lookout.
  • Johnson:
    1. If Nixon is not the safecracker, then I am.
    2. Ford is not the wheelman.
  • Nixon:
    1. I am not the lookout.
    2. Kennedy is not the mastermind.
  • Ford:
    1. If Johnson is the wheelman, then Nixon is the lookout.
    2. Kennedy's second statement is false.
  • Reagan:
    1. Nixon's first statement is true.
    2. Ford's first statement is false.
Can you determine who the triggerman was?

I will post answers next week. Feel free to post your solutions in the comments.

4 comments:

  1. This comment has been removed by the author.

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  2. I think the shooter was Alfie. simone

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  3. *********************SPOILERS*********************

    I'm going to politely disagree with Simone and say that Benjy was and all of them but him were telling the truth.

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  4. 1. James Wilson
    2. Benjy; all but one told the truth
    3. Triggerman was Ford.
    Oh and there was this quote at the end of the blog post, "Feel free to post your solutions in the comments." So there's really not any need to post spoilers Trevor; I doubt anybody's actually going to look through the comments not looking for answers.

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