Saturday Puzzle #11 – Einstein’s Puzzle

Today’s puzzle is said to have been devised by Albert Einstein, who supposedly claimed that 98% of the population could not solve it. I haven’t researched the accuracy of this tale, but you can color me highly skeptical. Nevertheless, it’s a beautiful puzzle in the area of deductive reasoning. If you’ve seen this puzzle before you may notice that I’ve taken the liberty of modernizing it: men are replaced with women and cigarette brands are replaced with favorite musicians.

Assume there are five houses of different colors next to each other on the same street. In each house lives a woman of a different nationality. Each woman has a favorite drink, a favorite musician, and keeps a particular type of pet. All such attributes are unique – in other words, no two women share the same house color, nationality, pet, drink, or favorite musician.

Here are 15 facts you should know about this neighborhood:

  1. The Englishwoman lives in the red house.
  2. The Swede keeps dogs.
  3. The Dane drinks tea.
  4. The green house is just to the left of the white one (from in front of the houses).
  5. The owner of the green house drinks coffee.
  6. The Springsteen fan keeps birds.
  7. The owner of the yellow house likes Frank Sinatra.
  8. The woman in the center house drinks milk.
  9. The Norwegian lives in the leftmost house.
  10. The Beatles fan lives next to a woman who keeps cats.
  11. The woman who likes Elvis drinks beer.
  12. The woman who keeps horses lives next to the woman who likes Sinatra.
  13. The German likes Lady Gaga.
  14. The Norwegian lives next to the blue house.
  15. The Beatles fan lives next to a woman who drinks water.

Here’s the challenge: tell me who owns the pet fish.

Hint: A good methodology for tackling this one is to create a 5 by 5 table on a piece of scrap paper, like this:

House 1 House 2 House 3 House 4 House 5
Color
Nationality
Drink
Musician
Pet

Then, print out this article and work on the facts above. When you make one or more deductions from one of the facts, insert the new information into your table and cross that fact off the list. Eventually, you will have no facts left to work on and a nearly full table, at which point the answer will be apparent.

Don’t worry if don’t manage to solve this one – studies have shown that just trying to tackle this sort of problem makes you smarter!

Solution: Congratulations to Mudassir Ansari, who deduced the correct answer. Here’s an annotated sequence of deductions (houses are numbered 1-5, left to right):

  • The woman in the center house drinks milk – so house 3 occupant drinks milk
  • The Norwegian lives in the leftmost house – so house 1 occupant is Norwegian
  • The Norwegian lives next to the blue house – so house 2 is blue
  • The green house is just to the left of the white one (from in front of the houses) – so house 3 or 4 green (and 4 or 5 is white)
  • The owner of the green house drinks coffee – house 3 occupant drinks milk so house 4 is green, house 5 is white and house 4 occupant drinks coffee
  • The Englishwoman lives in the red house – all but house 3 have conflicting color or nationality so house 3 is red and occupied by englishwoman and house 1 must be yellow
  • The owner of the yellow house likes Frank Sinatra – so house 1 occupant listens to Sinatra
  • The woman who keeps horses lives next to the woman who likes Sinatra – so house 2 occupant keeps horses
  • The Dane drinks tea – all but 2 houses have conflicts so the Danish tea drinker must live in house 2 or 5. This is tricky part: in order to resolve whether the Dane lives in house 2 or 5, I tried placing her in each house to see if a contradiction arises. If you try putting the Danish tea drinker in house 5, then by this rule: “The woman who likes Elvis drinks beer”, house 2 must be occupied by the beer drinking Elvis fan. At that point there’s only one missing drink so the house 1 occupant (the Sinatra fan) must drink water but that contradicts the rule that says “The Beatles fan lives next to a woman who drinks water”. We have arrived at a logical contradiction, which means our hypothesis must be wrong – the Danish tea drinker cannot live in house 5. The only alternative is to place the Danish tea drinker in house 2.
  • The woman who likes Elvis drinks beer – all but house 5 have conflicting musicians or drinks so house 5 must be the home of the beer drinking Elvis fan and there’s only one empty drink left so house 1 occupant must drink water
  • The Beatles fan lives next to a woman who drinks water – so house 2 occupant likes the Beatles
  • The German likes Lady Gaga – all but house 4 have conflicting nationalities or musicians so house 4 occupant likes Lady Gaga. Only one nationality left (so a Swede must live in house 5) and only one musician left (so house 3 occupant must like Springsteen)
  • The Swede keeps dogs – so house 5 occupant keeps dogs
  • The Springsteen fan keeps birds – so house 3 occupant keeps birds
  • The Beatles fan lives next to a woman who keeps cats – so house 1 occupant keeps cats

At last, there is only one empty cell in your table. It’s the only unclaimed pet, which is fish, and it belongs to the German, coffee drinking, Lady Gaga listening woman in the green house (#4). For the record, here’s the finished table:

House 1 House 2 House 3 House 4 House 5
Color yellow blue red green white
Nationality Norwegian Danish English German Swedish
Drink water tea milk coffee beer
Musician Sinatra Beatles Springsteen Gaga Elvis
Pet cats horses birds fish dogs

4 thoughts on “Saturday Puzzle #11 – Einstein’s Puzzle”

  1. German woman owns the fish

    H1 H2 H3 H4 H5
    Color Yellow Blue Red Green White
    Nationality Norway Denmark English German Sweden
    Musician Sinatra Beatles Springsteen Lady Gaga Elvis
    Pet Cat Horses Bird Fish Dog
    Drink Water Tea Milk Coffee Beer

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