Einstein's riddle - Who has the Fish?

I spent some time reviewing the posts/responses to this riddle on this site.  Bravo to the youngsters who spent time and effort which led to the correct configuration for house colors, owners, drink and smoking preferences.

However, the answer that the 4th house which is green and owned by the German who drinks coffee and smokes Prince owns a FISH is incorrect.  The true answer is that there is not enough information in the clues to determine that ANYONE owns a fish. The German may own a hamster or an iguana or a snake.  All we can deduce is that the German does NOT own a bird, cat, dog or horse. 

The purpose of the riddle (and this is what prompted Einstein to predict that only 2% of the population would arrive at the correct conclusion) was to illustrate the difference between inference and true deductive reasoning.  There are 25 parameters to be solved for (5 house colors, 5 nationalities, 5 beverages, 5 smoke brands and 5 types of pets).  However the clues are carefully constructed to only allow for 24 of these parameters to be solved for.  You can infer from the question that the 5th pet is a fish, but it is still just an assumption and not a provable fact.

In a simple illustration, given that:

A<B and B<C    and

A=1 and C=3

What does B equal?

Some people might be tempted to say that B=2 - but this is wrong.  We really do not have enough information to say that. You might infer that since I used whole numbers as the given values of  A and C, that B must also be a whole number and therefore must be equal to 2. But the facts as stated mean that B can be equal to an inifinite number of values   1.9753, 2.245, 2.999999, etc.

In reality, the German owns a gerbil - I saw him buy it in the pet store.

It is just as reasonable to assume that the missing pet is a fish is it is reasonable to assume that the statements given are correct. It is a logic puzzle. Part of the puzzle is the question "who has the fish", which means that there is a fish to be found in one of the houses. We are also told that the house owners all have different pets. On finding that there is only one occupant whose pet cannot be determined, we can therefore deduce that he has the fish.

The second house is blue because the norwegian is in the first.  The green house can only be 3 or 4, and white can only be 4 or 5 because G is to the left of W.  Therefor the British who lives in a Red house can only live in 3 or 5.  Houses 3, 4, and 5 can only G, W, or R.  That means the Yellow house is 1.  The Norwegian smokes Dunhill and lives next to the owner of the horse.  The Swedish man has a Dog and can only live in 3, 4, or 5.  The owner of the Cat smokes Blend and can only live in 3, 4, or 5.  The man that smokes Pall Mall has a Bird and can only live in 3, 4, or 5.  So the Dog, Cat, and Bird live in either 3, 4, or 5. 

In conclusion the Fish can only live in house 1 which is the Norwegan.

Thank you