Einstein's Riddle: The Solution
Einstein's Riddle: Who owns the fish ?
Statement:
There are 5 houses of 5 different colors.
In each house lives a person of a different nationality.
Each of the 5 residents drinks a certain type of beverage, smokes a certain brand of cigar, and keeps a certain pet.
None of them have the same pet, smoke the same brand of cigar or drink the same beverage.
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 resident of the green house drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The resident of the yellow house smokes Dunhill.
8. The resident of the center house drinks milk.
9. The Norwegian lives in the first house.
10. The person who smokes Blends lives next to the one who keeps cats.
11. The person who keeps the horse lives next to the one who smokes Dunhill.
12. The person who smokes Bluemasters drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The person who smokes Blends has a neighbor who drinks water.
Solution:
Step 1. Determine the color and location of the houses given 1, 4, 5, 7, 8, 9, 11, and 14.
House 1: Yellow. Norwegian. DunHill.
House 2: Blue. Horses.
House 3: Red. Brit. Milk.
House 4: Green. Coffee.
House 5: White.
We know the middle house is a milk drinker. Since the Norwegian lives in the first house and lives next to the Blue house we know the 2nd house is Blue.
The resident of the Green house drinks tea so clearly the middle house cannot be Green. Only two adjacent houses with unknown colors remain (on the far right).
Hence, the 4th house must be Green and the 5th house must be White.
The Brit must live in the 3rd house, the Red house, since the Norwegian lives in the 1st house, which must be the Yellow house.
Step 2. Determine a summary of what is know to be truths.
* The Dane (a tea drinker) cannot live in Red (Milk) or Green (Coffee).
* The Dane must live in Blue or White since Norwegian lives in Yellow.
* The German (smokes Prince) must live in Blue, White. or Green.
* The German does not drink Beer (Bluemaster smoker drinks Beer).
* The Swede (dogs for pets) must live in the Green or White house (Blue has horses).
* The owner who smokes blends has a neighbor who drinks water.
* The 5th house (White), cannot have an owner who smokes blends since their only neighbor drinks Coffee not water. The 1st owner smokes Dunhill.
Therefore, either:
a) Owner #1 drinks water and their neighbor Owner #2 smokes blends or
b) Owner #2 drinks water and their neighbor Owner #3 smokes blends.
Since Owner #2 owns a horse they cannot smoke PallMall. We know Owner #2 or Owner #5 must smoke bluemasters since Owner #1 smokes DunHill and Owners #3 and #4 do not drink Beer.
Step 3. Find a contradiction given scenarios "a" and "b".
Consider scenario b. If owner #2 drinks water then owner #1 and owner #5 are left to drink the tea and the beer.
We know owner #2 or #5 smokes bluemasters and drinks beer. Hence, since owner #2 was assummed to drink water, owner #5 would be required to drink Beer.
This means Owner #1 must drink the tea. We know the Dane drinks the tea. Owner #1 is Norwegian.
Since a contradiction resulted scenario "a" must apply. Let's pursue scenario "a" and determine if a contradiction results.
If owner #2 smokes blends then owner #5 must smoke bluemasters and drink beer. Thus owner #1 must drink water and owner #2 must drink tea.
Hence owner #5 cannot be German, the German must be owner #2 or owner #5. No contradiction. To summarize then:
Dane is #2 or #5; Swede is #4 or #5; German is #2 or #4.
Step 4. Final deductions given known information.
Since owner #2 smokes blends that requires owner #4 to be German and to smoke Prince.
That results in owner #3 smoking PallMall and having birds for pets. Hence, owner #1 must own a cat.
Since owner #2 is drinking tea they must be the Dane. This means that owner #5 is the Swede and owns a dog.
Hence, the German owns the Fish.
No apparent contractions resulted. In summary then…
House 1. Yellow. Norwegian. DunHill. Water. Cat.
House 2. Blue. Dane. Blends. Tea. Horse.
House 3. Red. Brit. PallMall. Milk. Birds.
House 4. Green. German. Prince. Coffee. Fish.
House 5. White. Swede. BlueMaster. Beer. Dogs.
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