BLUE
The King’s Wise Men: This is one of the simplest induction puzzles and one of the clearest indicators to the method used.

• Suppose that there was one blue hat. The person with that hat would see two white hats, and since the king specified that there is at least one blue hat, that wise man would immediately know the color of his hat. However, the other two would see one blue and one white hat and would not be able to immediately infer any information from their observations. Therefore, this scenario would violate the king’s specification that the contest would be fair to each. So there must be at least two blue hats.
• Suppose then that there were two blue hats. Each wise man with a blue hat would see one blue and one white hat. Supposing that they have already realized that there cannot be only one (using the previous scenario), they would know that there must be at least two blue hats and therefore, would immediately know that they each were wearing a blue hat. However, the man with the white hat would see two blue hats and would not be able to immediately infer any information from his observations. This scenario, then, would also violate the specification that the contest would be fair to each. So there must be three blue hats.

Since there must be three blue hats, the first man to figure that out will stand up and say blue.

Source : https://en.wikipedia.org/wiki/Induction_puzzles

The answer is blue.

The king hasn’t decided which he wants to make his advisor so all the sages have to see the same thing to make it a fair test.

If his hat were blue both B and C would see two people with blue hats and cannot say which colour their hat would be due to the fact that the king did not specify about how many hats would be of each colour.

If his hat were white then, again, neither B nor C can deduce what colour their own hat is as the king didn’t specify as I said above.

If sage A had a white hat, then using your words, Sage A would be “Unique” but since the King cannot decide which Sage to chose it would have to be a fair test.

I may be wrong, but after thinking about it, this is the only logical explanation I could reach.

a) We know that Norwegian lives in the 1st house (Hint: #9) and next to him lives a  guy who stays in a blue house (Hint: #14). So far we have the following:

b) We know that the green house is on the left of the white house (Hint: 4), therefore we can form a new group with the Green and White house next to each other.

c) Now think carefully the combination of (a) and (b). We should reach to the conclusion that the Norwegean guy who lives in the first house, he either lives in the Red or Yellow house since the Green & White houses group can only have a position of either 3-4 or 4-5.

d) Since the Brit is the guy who lives in the Red house (Hint: 1), now we definitely know that the Norwegian lives in the Yellow house. So far we have the following information:

Group:

e) Next, we know that the owner of the Green house drinks coffee (Hint: 5) and the man living in the center house drinks milk (Hint: 8). As a result, we conclude that the group of Green and Yellow house are the 4th and 5th house in order and that the center house (number 3) is the Brit.

f) Hint 7 gives us another information on the first house (The owner of the yellow house smokes Dunhill). In-addition, the man who keeps the horse lives next to the man who smokes Dunhill (Hint 11), therefore the man living in house #2 keeps horses.

g) Hint 15 states that “The man who smokes Blend has a neighbor who drinks water.”  We conclude that only 2 people can have a neighbor who drinks water (House 1&2), but since House #1 already smokes Dunhill that means that House #2 smokes Blend and House #1 drinks water.

h) Hint 12 states “The owner who smokes Bluemaster drinks beer.” See the table above and you will notice that we are missing the drink only for houses 2 and 5 but since we already know that the owner of house 2 smokes Blend, then the combination of Hint 12 applies to house #5.

 i) Hint 3 states that “The Dane drinks tea.”. We are missing only the drink for house #2 therefore this applies to house #2.

j) Hint 10 states “The man who smokes Blend lives next to the one who keeps cats.” As a result, house #1 keeps cats since house #2 has the owner who smokes Blend.

k) Hint #13 states that “The German smokes prince”. We are missing the nationalities of the owners who live in house #4 and #5 but since the owner of house #5 smokes Bluemaster, this hint applies to house #4.

l) Hint #6 states that “The person who smokes Pall Mall rears birds”. We are only missing the tabacco of House #3 therefore:

m) Finally hint #2 states that “The Swede keeps dogs as pets”. This combination can only be applied to house #5.

n) Now who owns the fish? The German owns the fish!!!

Congratulations, according to Einstein you now belong to the 2% of the people who can solve this riddle!!!

source – http://einsteinriddle.com/index.php/einstein-s-riddle-solution-explained