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  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION          
COLOR          
DRINK          
CIGAR          
PET          








This is the way I solved the problem. There are probably other ways, too. You should check to make sure I got this right.

There are five houses. For each house, there are five bits of information about the house and its occupant: the house's color and the occupant's nationality, pet, favorite drink, and favorite cigar.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway        
COLOR          
DRINK          
CIGAR          
PET          








Fact 9: The Norwegian lives in the first house.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway        
COLOR   blue      
DRINK          
CIGAR          
PET          








Fact 14: The Norwegian lives next to the blue house.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway        
COLOR   blue      
DRINK     milk    
CIGAR          
PET          








Fact 8: The man living in the house right in the center drinks milk.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway        
COLOR   blue   green white
DRINK     milk coffee  
CIGAR          
PET          








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




This means the green and white houses are next to each other with the green on the left. As I'm writing this, I'm realizing that this is open to interpretation though -- maybe it just means that if you look at the five houses, the green one is to the left of the white one. But I can defend my choice with a quick piece of logic: my choice leads to only one solution. If my interpretation of the words is incorrect, my choice is still consistent with the more general interpretation. If the more general interpretation has only one solution, it must be mine. If the more general interpretation allows for more than one solution, then the problem would be indeterminate; since the problem implicitly claims to have a unique solution, this would be inconsistent. Thus I like my choice of interpretation.




Fact 5: The green house owner drinks coffee.




Together these two facts mean we have to fit a piece that looks like:

green white
coffee  
into the second two rows of the table. The only place it can fit is the fourth and fifth columns.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway   Britain    
COLOR   blue red green white
DRINK     milk coffee  
CIGAR          
PET          








Fact 1: The Brit lives in a red house.




This means we have to fit a piece that looks like:

Britain
red
into the first two rows of the table. The only place it can fit is the third column.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway   Britain    
COLOR yellow blue red green white
DRINK     milk coffee  
CIGAR          
PET          








The only place left for ``yellow'' is the first column.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway   Britain    
COLOR yellow blue red green white
DRINK     milk coffee  
CIGAR Dunhill        
PET   horses      








Fact 7: The owner of the yellow house smokes Dunhill.




Fact 11: The man who keeps horses lives next to the man who smokes Dunhill.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway   Britain    
COLOR yellow blue red green white
DRINK     milk coffee  
CIGAR Dunhill        
PET   horses      








Next comes a teensy bit of brute force.

We have three nationalities (German, Swede, and Dane) to put in three columns. Absent any further analysis, there are six ways to do so. However, we can use facts 2 and 3 to pare the list to just three ways.

For the heck of it, let's place the German first.

Suppose the German lives in house #2. Fact 3 tells us the Dane drinks tea so he cannot live in house #4. Thus the Swede is in house #4 and the Dane in #5.

Suppose the German lives in house #4. Fact 2 tells us the Swede keeps dogs as pets so he cannot live in house #2. Thus the Dane is in house #2 and the Swede in #5.

Suppose the German lives in house #5. Fact 3 tells us the Dane drinks tea so he cannot live in house #4. Thus the Dane is in house #2 and the Swede in #4.

We can also throw in fact 13 that the German smokes Prince cigars. All three possibilities are shown on the next page.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Germany Britain Sweden Denmark
COLOR yellow blue red green white
DRINK     milk coffee tea
CIGAR Dunhill Prince      
PET   horses   dogs  




  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK   tea milk coffee  
CIGAR Dunhill     Prince  
PET   horses     dogs




  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Sweden Germany
COLOR yellow blue red green white
DRINK   tea milk coffee  
CIGAR Dunhill       Prince
PET   horses   dogs  

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Germany Britain Sweden Denmark
COLOR yellow blue red green white
DRINK     milk coffee tea
CIGAR Dunhill Prince      
PET   horses   dogs  




  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK   tea milk coffee beer
CIGAR Dunhill     Prince Blue Master
PET   horses     dogs




  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Sweden Germany
COLOR yellow blue red green white
DRINK   tea milk coffee  
CIGAR Dunhill       Prince
PET   horses   dogs  








Next we'll look at fact 12: the owner who smokes Blue Master drinks beer. That means we need to fit the piece:

beer
Blue Master
into the third and fourth rows of the table. It can't fit into the first or third tables; we can toss them as possibilities.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK   tea milk coffee beer
CIGAR Dunhill     Prince Blue Master
PET   horses     dogs








This brings us to the above; only clues 6, 10, and 15 are left.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK   tea milk coffee beer
CIGAR Dunhill   Pall Mall Prince Blue Master
PET   horses birds   dogs








Clue 6 says that the person who smokes Pall Mall raises birds. That means we need to fit the piece:

Pall Mall
birds
into the last two rows of the table. Only the third column is a possibility.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK water tea milk coffee beer
CIGAR Dunhill Blend Pall Mall Prince Blue Master
PET cats horses birds   dogs








Clue 10 says we need the person who smokes Blend next to the one who keeps cats, and clue 15 says he also lives next to the person who drinks water (not necessarily the same one who keeps cats). We need one of the pieces:

water         water   water         water
  Blend or   Blend   or   Blend   or Blend  
cats     cats           cats     cats
                         
in the last three rows of the table. Only the set of cells on the left offers a possibility.

  HOUSE #1 HOUSE #2 HOUSE #3 HOUSE #4 HOUSE #5
NATION Norway Denmark Britain Germany Sweden
COLOR yellow blue red green white
DRINK water tea milk coffee beer
CIGAR Dunhill Blend Pall Mall Prince Blue Master
PET cats horses birds fish dogs








That's all the clues. The only spot left is the pet that the German keeps: fish!




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James Michael Rath 2004-04-16