Einstein's Puzzle

Submitted by Bill St. Clair on Mon, 26 Dec 2005 13:35:10 GMT

Einstien supposedly created the following puzzle:

There are 5 houses in 5 different colours. In each house lives a person of a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. Using the clues below can you determine who owns the fish?

The Brit lives in a red house.
The Swede keeps dogs as pets.
The Dane drinks tea.
The green house is on the immediate left of the white house.
The green house owner drinks coffee.
The person who smokes Pall Mall rears birds.
The owner of the yellow house smokes Dunhill.
The man living in the house right in the middle drinks milk.
The Norwegian lives in the first house.
The man who smokes Blend lives next door to the one who keeps cats.
The man who keeps horses lives next door to the man who smokes Dunhill.
The owner who smokes Blue Master drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
The man who smokes Blend has a neighbour who drinks water.

Here's my solution. Stop reading now if you want to work it out yourself.

First off, it's necessary to assume that the "first house", in which the Norwegian lives, is on the far left. I haven't worked it out if you assume that it's on the far right.

Since the green house owner drinks coffee, the green house cannot be in the middle, as its owner drinks milk.

The second house is blue, hence, since the green house is on the immediate left of the white house, it must be in position 4 (counted from the left). Since the brit lives in the red house, the Norwegian must live in the yellow house. This means that the houses are in the following order, with known relationships in parentheses:

yellow (Norwegian, Dunhill), blue (horses), red (Brit, milk), green (coffee), white

And here are the remaining clues, shortened for ease off use, and organized as smoke, pet, drink, and nationality:

Pall Mall, birds
Blend next to cats and next to water
Blue Master, beer
Prince German

cats next to Blend
dogs Swede
fish

tea Dane
water next to Blend
beer next to Blue Master

German Prince
Swede dogs
Dane tea

Since the Blue Master smoker drinks beer, he must live in either the blue or white house. Assume he lives in the blue house. Then Blend is in the green house (it can't be next to water in the red or white), the Prince-smoking German is in the white house with his water, and the Brit smokes Pall Mall:

yellow (Norwegian, Dunhill), blue (Blue Master, beer, horses), red (Brit, Pall Mall, milk, birds), green (Blend, coffee), white (German, Prince, water, cats)

Now the Swede and his dogs must go in the green house, so there's no place for the Dane with his tea. Our Blue Master assumption must have been incorrect.

Backing up, The Blue Master smoker must be in the white house with his beer:

yellow (Norwegian, Dunhill), blue(horses), red(Brit, milk), green (coffee), white (Blue Master, beer)

Now Blend has to be either in the blue or red house (it can't be next to water in green or white). Assume its in the red house. Then water is drunk in the blue house, cats are kept in the green house, the Swede keeps his dogs in the white house, and once again there's no place for the Dane and his tea.

So, back up once again. Blend must be smoked in the blue house, the Norwegian drinks water, the Dane must live in the blue house with his tea, and the German must smoke his Prince in the green house.

yellow(Norwegian, Dunhill, water), blue(Dane, Blend, tea, horses), red(Brit, milk), green (German, Prince, coffee), white(Blue Master, beer)

The remaining unused clues are:

Pall Mall, birds
Blend next door to cats
Swede, dogs

So the Brit must smoke Pall Mall and keep birds, the Norwegian must keep cats, and the Swede must live in the white house with his dogs:

yellow (Norwegian, Dunhill, water, cats), blue (Dane, Blend, tea, horses), red (Brit, Pall Mall, milk, birds), green (German, Prince, coffee), white (Swede, Blue Master, beer, dogs)

Conclusion: the German owns the fish.

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Comments (4):

It isn't possible to do it

Submitted by Anonymous on Thu, 05 Jun 2008 21:15:28 GMT

It isn't possible to do it the other way round. It is also possible entirely from logical decisions rather than assumptions so you obviously happened to get lucky

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I found it alone with my

Submitted by Anonymous on Tue, 17 Jun 2008 15:28:39 GMT

I found it alone with my logic... it is possible

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I found it too. It is

Submitted by Anonymous on Thu, 02 Oct 2008 19:07:47 GMT

I found it too. It is possible, but you have to narrow down your guesses as the author did to a 50/50 chance of success.

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Standard proof technique

Submitted by Bill St. Clair on Thu, 02 Oct 2008 19:46:55 GMT

Standard proof technique. Assume X. Reason to a contradiction. Conclude not X.

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