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I was working with Einstein's riddle yesterday and after some time I figured out a solution. But then I thought. What if the whole neighbourhood is a circle? (If you played GTA San Andreas like Grove street). What if the 5 houses are in a circle and not a straight line. Would that give a different answer? Has anyone else ever thought of this?

If you do not remember the full riddle here it is:

1. There are 5 houses in 5 different colours. In each house lives a person with a different nationality.
2. The 5 owners drink a certain type of beverage, smoke a certain brand, and keep a certain pet.
3. No owners have the same pet, smoke the same brand of cigar/cigarette or drink the same beverage.


The question is "Who owns the fish?"


Facts: 

The Brit lives in the red house
The Swede keeps dogs as pets
The Dane drinks tea
The green house is to the left of the white house
The green house's owner drinks coffee
The person who smokes Pall Mall rears birds
The owner of the yellow house smokes Dunhill
The man living in the centre house drinks milk
The Norwegian lives in the first house
The man who smokes Blends lives next to the one who keeps cats
The man who keeps the horse lives next to the man who smokes Dunhill
The owner who smokes Bluemasters drinks beer
The German smokes Prince
The Norwegian lives next to the Blue House
The man who smokes blends has a neighbour who drinks water
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    $\begingroup$ I can assure you that I do not remember the full riddle ;-) $\endgroup$ – Matemáticos Chibchas Sep 22 '13 at 18:46
  • $\begingroup$ This is why I included it in the question :D $\endgroup$ – John Demetriou Sep 22 '13 at 20:05
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Since no rule is about people not being neighbors, it is immediately clear that any solution to the original riddle will also be a solution to the new one, but there can be other solutions that do not solve the original riddle.

The facts that the Norwegian lives in the first house and that the man in the centre house drinks milk become slightly odd when the houses are placed in a circle, although no real contradictions arise. The facts can be interpreted as that the Norwegian has house number 1, and the man in the third house drinks milk (this interpretation merges these rules into a single rule: Neither the Norwegian nor his two neighbors drink milk).

As for the solution, it is not unique under the new condition. In fact, the original riddle is a bit ambiguous, as it is not really clear if the first house is the leftmost or the rightmost house (although the only difference in the two solution is the order of the houses). The solution if the first house is to the left is:

 Yellow     Blue    Red        Green   White
 Norwegian  Dane    Brit       German  Swede
 Cats       Horse   Birds      Fish    Dogs
 Water      Tea     Milk       Coffee  Beer
 Dunhill    Blends  Pall Mall  Prince  Bluemasters

If the first house is to the right, the houses look the same (so the same person owns the fish) but they are in the order

green, white, red, blue, and yellow.

Both of these solutions (which ultimately give the same answer to the riddle) are of course allowed when the houses are placed in a circle, as well as the following solutions, which give a different owner of the fish:

 Yellow     Green   White        Red        Blue
 Norwegian  German  Swede        Brit       Dane
 Cats       Horse   Dogs         Birds      Fish
 Water      Coffee  Beer         Milk       Tea
 Dunhill    Prince  Bluemasters  Pall Mall  Blends

and

 Green      White   Red     Yellow   Blue
 Norwegian  German  Brit    Dane     Swede
 Birds      Cats    Horse   Fish     Dogs
 Coffee     Water   Milk    Tea      Beer
 Pall Mall  Prince  Blends  Dunhill  Bluemasters

In conclusion: The riddle makes sense with the new condition, but it lacks a unique solution.


The only question remaining is

if there are solutions where the Norwegian or the Brit owns the fish (of course the Swede cannot own the fish, since he owns the dogs),

but it's getting late.

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