A traveler has to pass tests of increasing difficulty to meet an Eastern mystical master. For the first test, he meets a pair of twins at a fork in the road: one path leads to the jungle, the other to the mystic. One of the twins always says the truth, the other always lies. What yes/no question should you ask one of the twins to determine the path that goes to the mystic? For the second test, the traveler encounters a second fork in the road. Again, one path leads to the jungle, the other to the mystic. This time, there are three look-alike brothers: one always tells the truth, the second always lies but the third sometimes tells the truth and sometimes lies. What two Yes/No questions should the traveler ask two of the brothers to determine the path to the mystic? Each question is answered by only the brother it is posed to. For the second question, the traveler may choose the brother and the question depending upon the answer to the first question.
Logic puzzles like these are the brainchild of Raymond Smullyan, a famous logician who has devised hundreds of them to illustrate key theorems in logic through series of puzzles! The three-brother problem above was borrowed from The Puzzle Toad, Number 14 — Restrooms. Many more puzzles are to be found in books by Robert Smullyan.
The two-brother problem may be solved in two different ways:
Solutions to the three-brother problem:
The Knights and Knaves Puzzle Generator has 382 puzzles that you might enjoy. An exhaustive analysis of Knights and Knaves puzzles — "This page is not meant for human consumption" :-) Knights and Knaves (wikipedia) and The Hardest Logic Puzzle Ever (wikipedia). Three (easy but fun) puzzles, compiled by Salvador Gutierrez.
An Interesting Puzzle: "In a room there are 100 people, numbered from 1 to 100. A person is either a knight or a spy. Knights always tell the truth, but spies may tell the truth or lie as they see fit. Every person knows the identity of everyone else. It is known that there are strictly more knights than spies present. Asking only questions of the form `Person i, what is the identity of person j?', what is the minimum number of questions which will guarantee to find everyone's true identity?" Solution by Mark Wildon at Swansea University.