Five Houses Puzzle
[ Issue 40 ]

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Five Houses Puzzle

Tony Rogers shows that both logic and trial-and-error can be successfully used to solve the Five Houses Puzzle.  Stand by for a step-by-step solution.
 

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The Five Houses Puzzle and How to Solve It
ó Tony Rogers

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There is a row of five houses painted in five different colours. In each house lives a person with a different nationality. The owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain kind of pet. No owners have the same pet, smoke the same brand of cigar or drink the same beverage.

Who owns the fish?

Here are fifteen clues:

  1. The Brit lives in the red house.

  2. The Swede keeps dogs as pets.

  3. The Dane drinks tea.

  4. The green house is on the left of the white house.

  5. The green houseís owner drinks coffee.

  6. The person who smokes Pall Mall rears birds.

  7. The owner of the yellow house smokes Dunhill.

  8. The man living in the centre house drinks milk.

  9. The Norwegian lives in the first house.

  10. The man who smokes Blends lives next door to the one who keeps cats.

  11. The man who keeps the horse lives next door to the man who smokes Dunhill.

  12. The owner who smokes Blue Masters drinks beer.

  13. The German smokes Prince.

  14. The Norwegian lives next door to the blue house.

  15. The man who smokes Blends has a next-door neighbour who drinks water.

This is an example of what we might call ďmultiple-attributeĒ puzzles. Here we have a five-by-five challenge:

five colours
five nationalities
five drinks
five cigars
five pets.

The solution is arrived at by using a combination of logic and trial-and-error, mainly logic. Many of the clues are interdependent, which makes solving the puzzle confusing at first.

Nevertheless, the puzzle cannot be solved without relying on this interdependence.

The first thing towards finding a solution should be to draw a picture of the street, calling the houses A, B, C, D and E, with the Colour, Nationality, Drink, Cigar and Pet attributes running vertically, in that order.

Next, we fill in any obvious items, as follows,

From Clue 9, we can place the Norwegian in house A,
from Clue 14, we can colour house B Blue,
from Clue 8, we can place the Milk drinker in house C:

A B C D E
 

Blue

     

Norwegian

       
   

Milk

   
         
         

Now, looking at Clue 4, we try to locate the Green and White houses. They canít be either (A ó B) or (B ó C), because B is Blue.

Nor can Green and White be (C ó D). Why? Because Clue 5 puts the Coffee drinker in the Green house and house C has a Milk drinker. It follows that the Green house is D and the White is E.

This leaves us to find the Colour of houses A and C.

Because Clue 1 puts the Brit in the Red house, and House A has a Norwegian, we can deduce that House C is Red and House A is Yellow.

And while weíre at it, we can place the Dunhill smoker in his house (Clue 7), the Brit in his (Clue 1), the Coffee drinker in his (Clue 5) and the Horse owner in his (Clue 11):

A B C D E
Yellow

Blue

Red Green White

Norwegian

  Brit    
Dunhill  

Milk

Coffee  
         
 

Horse

     

We are now over 40% done, but from here on it gets a little more difficult.

Letís try to place the other drinks ó Beer, Water and Tea.

Taking house A, it canít be Tea drunk here because the Tea drinker isn't Norwegian but Danish (Clue 2). Likewise, it canít be Beer in house A because the beer drinker smokes Blue Masters (Clue 12) whereas the Norwegian in house A smokes Dunhill. House A must therefore have the Water drinker.

From this and Clue 15 it follows that the Blends smoker lives in house B.

Now, what is the nationality of the owner of house B?

Either German, Swedish or Danish. But he canít be German (Prince smoker, from Clue 13), since house Bís owner smokes Blends. Nor can he be Swedish (Dog owner, from Clue 2), since house Bís owner keeps a horse. So house B must be the Daneís, who from Clue 3 is the Tea drinker.

The Beer drinker (and Blue Masters smoker, from Clue 12) must therefore live in house E. This cannot be the German, from Clue 13, and thus has to be the Dog owning Swede (Clue 2), leaving house Dís owner as the Prince smoking German.

This means that the Brit in house C must smoke Pall Mall and is therefore the Bird fancier (Clue 6):

A B C D E

Yellow

Blue

Red

Green

White

Norwegian

Dane

Brit

German

Swede

Water

Tea

Milk

Coffee

Beer

Dunhill

Blends

Pall Mall

Prince

Blue Masters

 

Horse

Birds

 

Dogs

Finally, Clue 10 reveals that the next-door neighbour of the Blends smoker who keeps cats must live in house A.

From that, who owns the Fish becomes obvious.

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