Question

In: Math

1.     There are 5 houses in 5 different colors. 2.         A person of a different...

1.     There are 5 houses in 5 different colors.

2.         A person of a different nationality lives in each house.

3.         These 5 owners drink a certain beverage, eat a certain type of bread, and have a certain pet.

4.         No owners have the same pet, eat the same type of bread, or drink the same drink.

5.        Use the clues below to determine who keeps the fish.

CLUES

1.         The American lives in a red house.

2.         The Italian keeps dogs as pets.

3.         The Bahamian drinks tea.

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

5.         The green house owner drinks coffee.

6.         The person who eats sesame semolina bread rears birds.

7.         The owner of the yellow house eats black jack bread.

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

9.         The Norwegian lives in the first house.

10.       The man who eats pumpernickel bread lives next to the one who keeps cats.

11.       The man who keeps horses lives next to the man who eats black jack bread.

12.       The owner who eats sourdough bread drinks lemonade.

13.       The German eats brioche bread.

14.       The Norwegian lives next to the blue house.

15.       The man who eats pumpernickel bread lives next to the man who drinks water.

Solutions

Expert Solution

Well, we know from examining the clues and the question that:

  • The possible nationalities are:
    • American
    • Norwegian
    • Italian
    • Bahamian
    • German
  • The possible colors are:
    • Red
    • Green
    • White
    • Yellow
    • Blue (Assumption)
  • The possible beverages are:
    • Tea
    • Coffee
    • Milk
    • Lemonade
    • Water
  • The possible breads are:
    • Sesame semolina bread
    • Black jack bread
    • Pumpernickel bread
    • Sourdough bread
    • Brioche bread
  • The possible pets are:
    • Dogs
    • Birds
    • Cats
    • Horses
    • Fish

Well, we know there are five houses. We'll assume they're all in a row, and are numbered from left to right. We know the Norwegian is in the first house:

House #1 #2 #3 #4 #5
Nationality Norwegian ? ? ? ?
Color ? ? ? ? ?
Beverage ? ? ? ? ?
Bread ? ? ? ? ?
Pet ? ? ? ? ?

Since the American lives in the red house, the Norwegian can't. We also know the Norwegian lives next to the blue house, so his house isn't blue. We also know that the green house is to the left of the white house; the Norwegian can't live in the white house since there is no house to the left, and can't live in the green house because his only neighbor, the one to the right, is known to live in the blue house. Therefore, the Norwegian lives in the yellow house.

We also know the owner of the yellow house eats Black jack bread, and that the Norwegian has a neighbor with a blue house (the Norwegian only has one neighbor, to the right.)

So here's what our matrix looks like now:

House #1 #2 #3 #4 #5
Nationality Norwegian ? ? ? ?
Color Yellow Blue ? ? ?
Beverage ? ? ? ? ?
Bread Black jack ? ? ? ?
Pet ? ? ? ? ?

The man who keeps horses lives next to he man who eats Black jack bread; so the horse owner lives in the blue house. The center house's owner drinks milk, the green house's owner drinks coffee, and the green house is to the left of the white house. Since we know the left two houses are the yellow and blue houses, the only position for the green and white are green as the fourth and white as the fifth, since the middle (third) drinks milk and the owner of the green house drinks coffee. The middle house has to be red, and therefore is the American's. So now this is what we know:

House #1 #2 #3 #4 #5
Nationality Norwegian ? American ? ?
Color Yellow Blue Red Green White
Beverage ? ? Milk Coffee ?
Bread Black jack ? ? ? ?
Pet ? Horse ? ? ?

The owner who eats Sourdough bread drinks lemonade; since we know what houses #3 and #4 drink [and neither are lemoade] and we know what house #1 eats [and its not Sourdough bread], the only possibilities are houses #2 and #5. Keep this information in mind. Since it is evident house #1 cannot drink lemonade (only house #2 or #5 can), the only possible beverages for house #1 are water and tea, but since the Bahamian drinks tea, house #1 drinks water. The man who eats Pumpernickel bread lives next to someone who drinks water; the only house next to #1 (the water-drinking house) is #2. The man who eats Pumpernickel bread lives next to the one who has cats; so the cat-house is #1 or #3.

House #1 #2 #3 #4 #5
Nationality Norwegian ? American ? ?
Color Yellow Blue Red Green White
Beverage Water L/T? Milk Coffee L/T?
Bread Black jack Pumpernickel ? ? ?
Pet Cat? Horse Cat? ? ?

Since the Bahamian drinks tea, he must live in either house #2 or #5. The Italian and German could live in house #2, #4 or #5.

House #1 #2 #3 #4 #5
Nationality Norwegian B/I/G? American I/G? B/I/G?
Color Yellow Blue Red Green White
Beverage Water L/T? Milk Coffee L/T?
Bread Black jack Pumpernickel ? ? ?
Pet Cat? Horse Cat? ? ?

We know the lemonade-drinker eats Sourdough bread. The only houses that could drink lemonade are #2 and #5, but since we know that #2 eats Pumpernickel bread, #5 must be the house which drinks lemonade and eats Sourdough bread, and #2 has to be the house that drinks tea and the house of the Bahamian. We can eliminate the possibility of the Bahamian's residence being house #5.

House #1 #2 #3 #4 #5
Nationality Norwegian Bahamian American I/G? I/G?
Color Yellow Blue Red Green White
Beverage Water Tea Milk Coffee Lemonade
Bread Black jack Pumpernickel ? ? Sourdough
Pet Cat? Horse Cat? ? ?

We know the German eats Brioche bread. Therefore, he could not live at house #5 and therefore has to live at house #4. The Italian must live at house #5; we also know house #5 raises dogs since we know the Italian raises dogs, and that house #4 eats Brioche bread since the German eats Brioche bread.

House #1 #2 #3 #4 #5
Nationality Norwegian Bahamian American German Italian
Color Yellow Blue Red Green White
Beverage Water Tea Milk Coffee Lemonade
Bread Black jack Pumpernickel ? Brioche Sourdough
Pet Cat? Horse Cat? ? Dogs

The only possibility for house #3's eating is Sesame semolina bread; all of the others are taken. We know that whoever eats Sesame semolina bread raises birds; so house #3 raises birds, and house #1 therefore has cats, since the only houses which could have had cats were #1 and #3, and #3 has been eliminated.

House #1 #2 #3 #4 #5
Nationality Norwegian Bahamian American German Italian
Color Yellow Blue Red Green White
Beverage Water Tea Milk Coffee Lemonade
Bread Black jack Pumpernickel Sesame semolina Brioche Sourdough
Pet Cat Horse Birds ? Dogs

The only remaining pet is the fish, which must be owned by the German. We now know who owns the fish, and have solved the puzzle.

The completed matrix of data is as follows:

House #1 #2 #3 #4 #5
Nationality Norwegian Bahamian American German Italian
Color Yellow Blue Green Red White
Beverage Water Tea Milk Coffee Lemonade
Bread Black jack Pumpernickel Sesame semolina Brioche Sourdough
Pet Cat Horse Birds Fish Dogs

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