Thread: Classic: Hats puzzle View Single Post
 2005-10-15, 15:48 #2 S80780   Jan 2003 far from M40 1758 Posts Obviously, the 10th person has a 50% chance to survive, as noone except the monster can see his/her hat's colour. Nonetheless, the person is able to see all the other 9 hats. As 9 is odd, there must be an odd number of either white or black hats remaining. So, by "guessing" the color which appears an odd number of times, the 10th person survives with 50% chance and gives away all information needed to save the remaining 9. The (2n+1)th person survives by confirming his/her neighbour's choice, if that colour appears an even number of times among the remaining 2n hats, and altering it otherwise. The 2nth person survives by confirming his/her neighbour's choice, if that colour appears an odd number of times among the remaining (2n-1) hats, and altering it otherwise. If there were an odd number of inhabitants, the one who's asked first would have to "guess" a pre-agreed-upon colour, if his/her neighbour's hat has the colour that appears an odd number of times among the remaining ones, excluding his/her neighbour.