Source: Tanya Khovanova’s Math Blog
Problem: The king has a countable number of wise men. The line starts from the left and is infinite in the right direction. The wise men are all facing to the right and they see the infinite tail of the line. Again, the king places either a black or white hat on each head and they can only say one of two words: black or white. Will they be able to devise a strategy beforehand that ensures that not more than one person makes a mistake?
Reference: This is a followup to the following problem http://pratikpoddarcse.blogspot.com/2009/08/cap-puzzle.html
Update(24/01/10): Solution: Posted by me in comments (taken from a recent blog entry by Saurabh Joshi, IIT Kanpur)