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Friday, July 8, 2016

Einstein's Problem / Zebra Puzzle (Solved)

It feels like a decade has passed since I'd solved a good,tiring logical problem.I had come across this a number of times in the past two years but I felt like solving it today.So,here is the solution (in as much details as I could provide.)The problem itself was an exasperating one.It took me some time to think,explore,note down.It was definitely the best logic problem I've solved till date.



There are 5 houses sitting next to each other, each with a different 
color, occupied by 5 guys, each from a different country, 
and with a favorite drink, cigarette, and pet.  Here are the facts:

  1. The British occupies the red house.
  2. The Swedish owns a dog.
  3. The Danish drinks tea.
  4. The green house is on the left of the white house.
  5. The owner of the green house drinks coffee. 
  6. The person who smokes "Pall Mall" owns a bird.
  7. The owner of the yellow house smokes "Dunhill".
  8. The owner of the middle house drinks milk.
  9. The Norwegian occupies the 1st house.
  10. The person who smokes "Blend" lives next door to the person who owns a cat.
  11. The person who owns a horse live next door to the person who smokes "Dunhill".
  12. The person who smokes "Blue Master" drinks beer.
  13. The German smokes "Prince".
  14. The Norwegian lives next door to the blue house.
  15. The person who smokes "Blend" lives next door to the person who drinks water.


The question is: Who owns the fish?







Solution


ONE      TWO     THREE      FOUR      FIVE

Any of the 5 is any of the house,with any colour.
Check.


The only substantial clue you have empirical certainty about is the fourth.That either of the first four is the green house (since it is on the left of the white house) and either one of the last four (i.e two to five) is the white house.
The next point that gives you empirical certainty as well is the ninth.That the first house (House ONE) is occupied by the Norwegian.
The third (assertive) point is that the Norwegian lives next door to the blue house.So,the second house (House TWO) is the blue house.

At the end of this stage,we know these CERTAINTIES :-

The British occupies the red house.
The first house is that of the Norwegian.
The second house is blue.
Either of the first four houses are green and either of the last four houses are white.

Now,since the second house (House TWO) is blue,House ONE cannot be white or green.
So,it has to be that either the third house or fourth house is green and the fourth or fifth house is white.

Visually,it would look like this :- 

Norwegian      Blue      G/W      G/W      W


In the second phase,we would be intertwining multiple clues to reach our conclusion.


The owner of the green house drinks coffee. 
The owner of the middle house drinks milk.

So,the middle house is not the green house.Therefore,the fourth house is the Green house.And the fifth is the white house.

Norwegian      Blue      ......      Green      White

Now,the British own the Red house.So,the yellow house has to belong to the Norwegian.

Therefore,we have :-

Yellow      Blue      ......      Green      White

The only house left is the Red.

Hence,


Yellow      Blue      Red      Green      White

Norwegian      ......      British      ......     ......

Going by the other clues,we have :-


Yellow      Blue      Red      Green      White








Norwegian     ......      British      ......      ......




......      ......      Milk      Coffee      ...... 

Dunhill       ......       ......       ......       ......
......      Horse      ......       ......       ......

In the second phase,check mark those clues which have already been used.

  1. The British occupies the red house.
  2. The Swedish owns a dog.
  3. The Danish drinks tea.
  4. The green house is on the left of the white house.
  5. The owner of the green house drinks coffee. 
  6. The person who smokes "Pall Mall" owns a bird.
  7. The owner of the yellow house smokes "Dunhill".
  8. The owner of the middle house drinks milk.
  9. The Norwegian occupies the 1st house.
  10. The person who smokes "Blend" lives next door to the person who owns a cat.
  11. The person who owns a horse live next door to the person who smokes "Dunhill".
  12. The person who smokes "Blue Master" drinks beer.
  13. The German smokes "Prince".
  14. The Norwegian lives next door to the blue house.
  15. The person who smokes "Blend" lives next door to the person who drinks water.

Colour : YBRGW
Nationality : N_B_ _
Drink : _ _ MC_
Cigarette : D_ _ _ _
Pet : _ H _ _ _

In the third phase,when there are only two alternatives left,and the rest has been solved (which is,very well the basis of Mathematical logic - either yes,or no.There is nothing inbetween.) ; Go ahead and use trial and error method.


Now,Blend can be smoked by someone from the second,third or fifth house.And 
tea can be drank in the second or fifth houses.
By trial and error method,is we choose the fifth for tea,then Norwegian drinks tea,which is not possible since the Danish drinks it.Therefore,if we choose Tea for the second house owner,and thus tag him Danish,we have :-



Colour : YBRGW

Nationality : NDB_ _
Drink : _ TMC_
Cigarette : D_ _ _ _
Pet : _ H _ _ _

Now,Blend is smoked by someone who lives next door to the person who drinks water.Again by trial and error method,we have two options for the water drinker.If we choose the fifth house owner as the water drinker,we will reach the following solution :-


Colour : YBRGW

Nationality : NDBGS
Drink : WTMCB
Cigarette : Dunhill Blend Pall Mall Prince Blue Master
Pet : CHBFD

Which is the solution,and we conclude that the German owns the fish!










Problem Source : http://mathforum.org/
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4 comments:

  1. I loved the coherency with which you solved the puzzle, mine was more incoherent and halphazard.

    ReplyDelete
  2. Why make it so complicated? Draw a chart. Put every option in it, and cross off to eliminate all that don't fit. It's called possible worlds in logic.

    ReplyDelete
  3. Hi! Can you help me with this puzzle? https://www.brainzilla.com/logic/zebra/meeting-room/ I can't solve it and I believe it's harder than the einstein's riddle

    ReplyDelete

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