The Answer: "Einstein"'s 15 relations problem

I start by numbering the constraints to make it easier to refer to constraints while I am keeping notes.

1. The Englishman lives in the red house.
2. The Swed keeps dogs.
3. The Dane drinks tea.
4. The green house is just to the left of the white one.
5. The owner of the green house drinks coffee.
6. The Pall Mall smoker keeps birds.
7. The owner of the yellow house smokes Dunhills.
8. The man in the center house drinks milk.
9. The Norwegian lives in the first house.
10. The Blend smoker has a neighbor who keeps cats.
11. The man who smokes Blue Masters drinks beer.
12. The man who keeps horses lives next to the Dunhill smoker.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The Blend smoker has a neighbor who drinks water.

Start by filling in a constraint relation table with the values given directly by the constraints. Constraints:

8. The man in the center house drinks milk.
9. The Norwegian lives in the first house.
14. The Norwegian lives next to the blue house.

From constraint number 5 we can see that the center tile, which drinks milk, can not be a green house. So the fourth house from the left must be green, and the fifth white.

4. The green house is just to the left of the white one.
5. The owner of the green house drinks coffee.

The Englishman lives in a red house. We know that the far left house, or first house, is a Norwegian from constraint number 9, and given constraint 1 that an Englishman lives in a red house we know that the Norwegian's house is not red. So We now know that the Norwegian's house is not red,blue,green, or white so by process of elimination it is Yellow.

1. The Englishman lives in the red house.
9. The Norwegian lives in the first house.

Then by elimination the center house is Red. From constraint 1 it is also the Englishman's house

From constraint 7 we know that the Norwegian smokes Dunhills. From constraints we know that the person next to the Norwegian keeps horses, and becuase of the Norwegians corner location that must be the person in the Blue house.

7. The owner of the yellow house smokes Dunhills.
12. The man who keeps horses lives next to the Dunhill smoker.

From constraint 3 we know the Norwegian is not drinking Tea, from constraint 5 we know he does not drink coffee, and from constraint 8 we know he does not drink milk. That means the Norwegian must drink either water or beer. Since the Norwegian does not smoke Blue Masters, we know from constraint 11 he does not drink beer. By elimination this means the Norwegian must drink water.

3. The Dane drinks tea.
5. The owner of the green house drinks coffee.
8. The man in the center house drinks milk.
11. The man who smokes Blue Masters drinks beer.

From constraint 15 we know that the person next to the Norwegian smokes Blend.

15. The Blend smoker has a neighbor who drinks water.

We already know the Norwegian and Brit, and from constraints 2 and 13 we know that the person in the blue house is neither Swed or German. By elimination that makes him a Dane.

2. The Swede keeps dogs.
13. The German smokes Prince.

We also know that the Dane drinks tea.

3. The Dane drinks tea.

By process of elimination we see that the person in the white house must drink beer. From constraint 11 we also know that they smoke Blue Masters.

11. The man who smokes Blue Masters drinks beer.

We know from constraint 13 that the German smokes Prince so he can not be the person in the white house, and by elimination he must live in the green house.

13. The German smokes Prince.

By elimination we can place the Pall Malls. Then by constraint 6 that lets us identify who keeps the birds. From a constraint 2 we are told the Swed keeps dogs.

2. The Swed keeps dogs.
6. The Pall Mall smoker keeps birds.

From constraint 10 we know that the Norwegian must keep cats, and then by elimination the German keeps the unknown pet, the fish.

10. The Blend smoker has a neighbor who keeps cats.