26 Mar 2007
A king has three sons.
To choose his successor he places his sons in a single file line all facing the same way:
o---> o---> o--->
The king has 5 hats:
He places a hat on each son's head from behind and says, "Without moving, the first son who can tell me what color hat he is wearing inherits the throne." After quite a while the first son in front of the line (who can see neither of his brothers) guesses and is correct.
What color hat was he wearing and how did he know?
(scroll down for answer)
The real key to the teaser is "after quite a while."
There are 3 white hats and 2 black.
The brother in the rear would seem to have the advantage because he can see his brothers' hats in front of him. If he saw two black hats he would naturally know he was wearing a white one. But he is silent.
That means the two brothers in front of him must be wearing either 2 white hats or 1 white hat and 1 black hat.
The brother in the middle would deduce this and if he saw a black hat in front of him he would know that he is wearing white. But he doesn't speak up. So the middle brother must see a white hat in front of him and is unsure if his is white or black.
So from the silence of both brothers the one in front must deduce that he is wearing a white hat.
Seems like two of the brothers get the raw end of the deal here, huh? I imagine I would just guess and take what comes of it. Or orchestrate a coup and take the throne my way.