frank sinatra was the first person to sing my way.
frank sinatra was the first person to sing my way.
who was the first person to sing my way?
frank sinatra
Na
Na
now, when the warden asks the first person to say a color, or in our new interpretation, a 0 or a 1, he simply calls out the label of the sequence he sees. given this information, everyone after him can determine exactly what his own hat color is. the second person sees all but the first digit of the sequence that the first person sees. thus, as far as he knows, there are two possible sequences the first person could have been labeling: one starting with a 0, and one starting with a 1. because of our labeling scheme, these two sequences would receive opposite labels, so based on what the first person says, the second person can determine which of the two possible strings the first person saw, and thus he can determine his own hat color. similarly, every later person in the line knows every digit of the sequence except the one corresponding to his own hat color. he knows those before him because they were called out, and those after him because he can see them. with this information, he can use the label called out by the first person to determine his own hat color. thus, everyone except the first person always guesses correctly.
hat puzzle