Can You Solve Einstein’s Puzzle?

Ever so often I’m asked: why do you love math so much? And every time for a split second, I ponder a love that has become second nature to me. It’s not the equations, formulas, proofs or theorems. It’s something intangible. It’s in the process.

Staring at a problem, waiting for a flash of insight as you slowly chip away at it. It’s like coming out of the fog. Some people panic because they can’t clearly see the road ahead and in turn they fear and hate math.

They believe that the fog means they aren’t good at math.

But I’m here to tell you that isn’t true. For me, a good problem is the fog rolling in. The thicker, the more challenging, the better.

Growing up I loved logic puzzles. Looking back, I think those 99 cent puzzle magazines taught me a great deal. They taught me reasoning, critical thinking and most of all how to solve problems one small step at a time.

The following is a classic logic problem attributed to Einstein. I guarantee it will be an excellent exercise in logical reasoning and requires you to break a large task into smaller, manageable components.

A Classic Logic Puzzle

There are five houses of different colors adjacent to one another on a road. In each house lives a man of different nationality. Each man has a favorite drink, a favorite brand of cigarettes, and keeps a different kind of pet.

Based on the following clues, who owns the fish?

• The Englishman lives in the red house.
• The Swede keeps dogs.
• The Dane drinks tea.
• The green house is just to the left of the white house.
• The owner of the green house drinks coffee.
• The Pall Mall smoker keeps birds.
• The owner of the yellow house smokes Dunhills.
• The man in the center house drinks milk.
• The Norwegian lives in the first house.
• The Blend Smoker has a neighbor who keeps cats.
• The man who smokes Blue Masters drinks bier.
• The man who keeps horses lives next to the Dunhill smoker.
• The German smokes Prince.
• The Norwegian lives next to the blue house.
• The Blend smoker has a neighbor who drinks water.

So give it a shot! And when you’re done come back and I’ll walk you through the solution.

The Solution

Let’s begin with the clearest clues.

Make a diagram of the five houses with the facts and options available.

What else do we know about the Norwegian?

Since the Norwegian is in the first house, the blue house must be the Norwegian’s neighbor to the right.

Because we know where the Norwegian lives and which house is blue, we can make use of any clues involving nationality or house color.

According to these clues, the Norwegian cannot live in the Red house, keep Dogs, drink Tea, or smoke Prince. Since it isn’t the Green house, the Norwegian also doesn’t drink Coffee. And the owner of the Blue house cannot possibly drink Coffee or smoke Dunhills. Eliminate these options from the diagram.

Therefore the color of the first house is either Yellow or White. Let’s check what we know about those house colors.

The first house cannot be white because there are no houses to the left of it. Therefore the first house must be yellow. Furthermore if the green house is to the left of the white house, the last house cannot be green and the center house cannot be white.

We also know:

The center house cannot be Green, so it must be Red. Carrying out the logic, the last house must be White and the fourth house Green.

Checking for any further clues involving house color we find:

Now that we know the Norwegian smokes Dunhills, we can use information about cigarette brands to make further deductions.

Then the man who keeps Horses must live in the Blue house since it is the only neighbor to the Dunhill smoker. Furthermore the Dunhill smoker cannot drink Beer or keep Birds since those attributes belong to other smokers.

Therefore the Norwegian must drink Water.

According to these clues, the Blends smoker must be the owner of the Blue house meaning that the owner of the White house must smoke Blue Masters. Also neither the Green or White houses can keep Cats.

So the man in the White house drinks Beer and the man in the Blue house drinks Tea.

So far we’ve solved all of the colors and drinks. Using the following clues we can complete the puzzle.

Fill out the implications of those clues to arrive at the solution.

Therefore, the German owns the fish.

The main lesson here is to remember that when you do not immediately know how to solve a problem focus on breaking it down into smaller parts that you can tackle. In time, you’ll be able to solve the entire problem.

Next Lesson: Strategic Division

Thanks for reading!

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