[Mathematical Logic (Miscellaneous).]

An investigation is underway regarding a stolen mustang. There are three suspects - Bill, Joe, and Sam. In court, Sam stated that Joe stole the mustang. Bill and Joe also gave testimonies, but no one remembered what they said, and all the records were lost. During the trial, it was revealed that only one of the defendants stole the mustang, and only that person gave truthful testimony. So, who stole the mustang?
Think about why Sam cannot be the thief.

## Solution

Sam cannot be the thief because the thief told the truth, while Sam, in this case, lied. Joe cannot be the thief because, in this case, Sam told the truth, and only the thief told the truth. Therefore, the thief is Bill.

On an island, there live knights who always tell the truth and liars who always lie. A traveler met three islanders and asked each of them: "How many knights are among your companions?". The first one answered: "None." The second one said: "One." What did the third one say?

## Hint

Think about whether the first responder can be a knight.

## Solution

Suppose the first one is a knight, then both of the others are liars, but then it turns out that the second one told the truth, so the first one is a liar. Now, the second one. Suppose he is a liar, then the third one must be a knight, and it turns out that the second one told the truth. Therefore, the second one is a knight. This, in turn, means that the third one is also a knight, and he said "One."