ThunderCloud

Yes, that's exactly right. With a few notes...

Yes, that's exactly right.

I'm not sure I follow you there.

I'm not sure I follow you there.

Two questions: (1) Do any of the following count as "words": non-English words, acronyms, proper nouns? (2) If a word is a palindrome (such as "eye"), does it count once or twice?

I think you've got it now. Glad you enjoyed it.

Almost there...

Answer If the two logicians are required to give up if they figure they would never know it, then the game would go as follows I see what you're saying

Answer If the two logicians are required to give up if they figure they would never know it, then the game would go as follows

Answer

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?

Here is a fun puzzle a college room mate once gave to me: You have two lengths of fuse, and a book of matches. You know that each fuse length has (somehow) been cut so that if the fuse is allowed to burn from end to end, it will take precisely 1 minute to burn down. However, the fuses will not necessarily burn at an even pace; all you know is the total combustion time of each fuse. Using nothing but the two lengths of fuse and the matches to ignite them with, how can you measure an interval of 45 seconds?