ThunderCloud

With a tip of the hat to itsmeee's 999 puzzle, and bonanvoa's Mad Hatter puzzle...

You come to a three-way fork in the road. You know that one path leads to your destination, and that the other two paths lead to Certain Doom™. You know that in the area is a tribe of truth-tellers and a tribe of liars, both of which will answer appropriately whenever they can, or remain silent whenever they cannot answer a question truthfully (or falsely). A tribesman from one of these tribes -- you know not which -- is standing at the fork, and -- as if for his own amusement -- offers to answer one single question with "Yes" or "No" to help you find your way. What question do you ask him?

This one isn't too hard, but is a fun exercise.

Two motor boats began speeding toward one another at the same time from opposite shores of a river. Upon reaching the opposing shore, each motor boat immediately reversed course and headed back to his original shore. In so doing, the motor boats passed each other twice. The first time they crossed, they were 700 feet from one shore of the river; the second time, they were 300 feet from the opposite shore. Assuming each boat traveled with constant speed, and neglecting any influence of river current, how wide is the river?

Although I believe the logic to answer the original problem was present, it was distributed among several postings... It did not seem right to mark any single post as the best answer. Therefore, here is the bonus round.

If approached correctly, this version is not much harder than the original.

The puzzle:

Three perfect logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e.1, 2, 3, ...), and that the sum of the integers on all three stickers is either 1002 or 1003. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' (or say "I don't know"). The question was repeated, again in turn, until EACH of the three logicians had either named their number or given up. All three stickers actually had the same number written on them. Who among the three logicians was able to deduce his number, and who among them gave up? (Furthermore, how did each answer?)

This puzzle is a variation on the "Hardest Logic Puzzle Ever", as can be seen on Wikipedia. I've found it to be a fun problem to play with.

There are three gods, each of whom speaks through his respective totem. One god always tells the truth, one always lies, and one answers entirely at random. The three totems are unlabeled, so you do not know which god is which. The gods respond only to yes-no questions, and may only be addressed individually via the querant's choice of totem. Furthermore, each god answers in his own personal language, and you know nothing in advance about any of the three gods' languages, save that each includes distinct words for "yes" and "no". Your task is to correctly ascribe each totem to its respective god with only three questions. What are your questions, and how are they directed?

Note: Because the "god of Truth" must always tell the truth, and the "god of Lies" must always lie, neither god is able to respond to a question which lacks a definite answer. The "god of Randomness", however, will respond to any question -- his response is unrelated to the content of the question, but is instead prompted by the fact that he was asked one.

Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?