## Truth That Lies

One evening Detective Radstein visited Professor Bock. He was hanging out in the kitchen and overheard a conversation between Professor Bock and his wife. It appeared that Mrs. Bock had discovered that all the cutlets she had prepared for the next day were missing. She asked her husband:

—Did you eat the cutlets?
—I ate soup, the professor replied.
—Oh well, the children were probably very hungry.

Detective Radstein smiled to himself. Many mathematicians have trouble making false statements. Some of them adjust to social situations by learning how to lie while formally telling the truth. Radstein calls them dodgers. Fortunately, dodgers only dodge a question when they are threatened. It was obvious that Professor Bock was such a dodger. He implied that he didn’t eat the cutlets, because he had soup for lunch. The detective was ready to bet \$10,000 that, in truth, the soup was just an appetizer to Professor Bock’s meal of cutlets.

Detective Radstein talked to his friend Professor Bock about this obsession mathematicians have to make true statements. Professor Bock agreed that many mathematicians are like that. In fact, all the faculty members in his department are either dodgers or pathological truth-tellers. Ironically, all other staff members at Professor Bock’s math department are liars.

A pathological truth-teller is another term that Detective Radstein uses to describe people who tell the truth no matter what. They never dodge. They answer a question exactly, often disregarding the context and purpose of the question. For example, when someone enters an elevator and asks a pathological truth-teller, “Is this elevator going up or down?” the answer s/he gets is “Yes.”

One day Professor Bock asked Detective Radstein for help, following a series of laptop thefts at his department. It was clear that the thefts were committed by someone working at the department and that the criminal acted alone.

Detective Radstein decided that the easiest starting point would be to ask everyone the same question: Did you steal the laptops? If a pathological truth-teller is the perpetrator, s/he would admit to the crime. A dodger would evade the question, but only if they are guilty. A liar is flexible: s/he might either answer the question with a lie or dodge with a lie. These are the first three answers the detective got from members of the department:

—Alice: No, I didn’t steal the laptops.
—Bob: Alice stole the laptops.
—Clara: Alice didn’t steal the laptops.

Who stole the laptops?

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1. #### L33tminion:

What I think the solution is:

1. Alice can be an innocent truth-teller, an innocent dodger, or a guilty liar. A guilty truth-teller would profess their own guilt, and neither an innocent liar or a guilty dodger would profess their own innocence when questioned directly.

2. Bob is dodging the question. But a dodger would dodge only if guilty, and only with a true statement, and that statement would not be true if Bob was guilty. A truth-teller wouldn’t dodge at all. Thus, Bob is a liar (who may or may not be guilty). So Alice is innocent.

3. Clara is also dodging the question, but with a truthful statement. So Clara is a guilty dodger, trying to evade justice without lying by professing someone else’s innocence.

Clara is a guilty dodger, Bob is an innocent* liar, and Alice is innocent and not a liar (though there’s no telling if Alice would dodge the question, were she the culprit).

* Innocent of stealing the laptops, anyways.

2. #### Areign:

Clara is a filthy dodger

3. #### Tanya Khovanova's Math Blog » Blog Archive » Dodgers, Liars and Pathological Truth-Tellers:

[…] of Deys University was very easy. This was due to a fact discovered by Detective Radstein on a previous case: every member of the department was one of three […]