Solved mathematical logic problems to practice reasoning
(0) Mathematical logic problems : Solutions 0.4
0.4 A hat box contains exactly 5 hats of the same size and shape, but three of them are white and the other two are black. 3 logicians decide to blindfold themselves and put on a hat at random with the intention of discovering the color of their hat by looking at their companions' hats. The first logician removes his blindfold and says "I don't know what color my hat is". The second one then removes his blindfold after looking at the first and says "Neither do I". To which the third logician, without removing his blindfold, states: obviously mine is white. How did the third logician deduce that his hat was white?
-Solution-
If A knows, then B and C have black hats. Therefore, if they don't know, at least one has white. This means that if C has black, then B has white. B knows this. B looks at C and doesn't know. If B knew, then C would have had black. C knows that A and B don't know, therefore, he knows that his is white.