Einstein's Puzzle

I saw an informal IQ test that is fun to do. It is called Einsteins’ Puzzle, although it is not clear whether it was Einstein who actually invented the test. I found it in http://sesquiq.thelogics.org/freeiqtests.html together with other tests, but a Google search for “Einstein’s test” will take you to many pages on the subject.

According to Larry Neal Gowdy, who wrote the page where I found the test, the time people take to solve the test is linearly correlated to their IQ percentile. Apparently, unless you are in the top 2% of IQ percentile (the level that qualifies you to join Mensa), you will never succeed in solving the puzzle!

Here is a graphic representation of what Gowdy said:

That is, according to Gowdy, somebody who scraped through the Mensa qualification test takes two hours to solve Einstein’s puzzle. If you want to try it out, start your timer immediately before reading the text of the test.

Here it is:

There are 5 houses in 5 different colors. In each house lives a man with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, nor drink the same beverage.

The Brit lives in the red house.

The Swede keeps dogs as pets.

The Dane drinks tea.

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

The green house's owner drinks coffee.

The person who smokes Pall Mall rears birds.

The owner of the yellow house smokes Dunhill.

The man living in the center house drinks milk.

The Norwegian lives in the first house.

The man who smokes Blends lives next to the one who keeps cats.

The man who keeps the horse lives next to the man who smokes Dunhill.

The owner who smokes Bluemasters drinks beer.

The German smokes Prince.

The Norwegian lives next to the blue house.

The man who smokes Blends has a neighbor who drinks water.

Who owns the fish?

If you give up and want to know how I solved it, keep reading.

First of all, I expressed the statements of the test in a compact form:

A. Brit - red

B. Swede - dogs

C. Dane - tea

D. green | White

E. green - coffee

F. birds - PallMall

G. yellow - Dunhill

H. center - milk

I. first - Norwegian

J. (cats) | Blends | (cats)

K. (Dunhill) | horse | (Dunhill)

L. beer - Bluemasters

M. German - Prince

N. (blue) | Norwegian | (blue)

O. (water) | Blends | (water)

I did it because I wanted to avoid being distracted by the wordiness of the original statements.

Then, I made a table with one column for each house position, from left to right.

We can immediately use I, H, and N to begin populating the table:

	1st	2nd	3rd	4th	5th
colour		blue
citizenship	Norwegian
pet
drink			milk
cigars

After combining D with E and J with O, we are left with:

A. Brit - red

B. Swede - dogs

C. Dane - tea

DE. green - coffee | White

F. birds - PallMall

G. yellow - Dunhill

JO. (cats) - (water) | Blends | (cats) - (water)

K. (Dunhill) | horse | (Dunhill)

L. beer - Bluemasters

M. German - Prince

DE tells us that green and coffee are on the left of white. This means that green cannot be in first position because otherwise it would have blue on its right. Obviously, it cannot be in second position either because it is green and not blue. And it cannot be in third position because its occupant drinks coffee and not milk. This means that green is in fourth position:

	1st	2nd	3rd	4th	5th
colour		blue		green	white
citizenship	Norwegian
pet
drink			milk	coffee
cigars

Then, red must be in third position because only two positions have an undefined colour, the first position is occupied by a Norwegian, and, according to A, red’s occupant is a Brit. Before redrawing the table, we can also write yellow in first position (the only position with undefined colour) and apply to it G:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian		Brit
pet
drink			milk	coffee
cigars	Dunhill

The remaining statements are:

B. Swede - dogs

C. Dane - tea

F. birds - PallMall

JO. (cats) - (water) | Blends | (cats) - (water)

K. (Dunhill) | horse | (Dunhill)

L. beer - Bluemasters

M. German - Prince

Now, statement K forces us to write horse in the second house because we know that Dunhill is in the first one:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian		Brit
pet		horse
drink			milk	coffee
cigars	Dunhill

And we are left with the statements:

B. Swede - dogs

C. Dane - tea

F. birds - PallMall

JO. (cats) - (water) | Blends | (cats) - (water)

L. beer - Bluemasters

M. German - Prince

According to C, Dane/tea can either be in the second house or in the fifth one. The same applies to beer/Bluemasters according to statement L. Therefore, we have two possible situations:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian	Dane	Brit
pet		horse
drink		tea	milk	coffee	beer
cigars	Dunhill				Bluemasters

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian		Brit		Dane
pet		horse
drink		beer	milk	coffee	tea
cigars	Dunhill	Bluemasters

The following statements remain to be applied:

B. Swede - dogs

F. birds - PallMall

JO. (cats) - (water) | Blends | (cats) - (water)

M. German - Prince

In either case, water must be in first position. This makes the second situation impossible, because statement JO stipulates that water is neighbouring Blends, while with the second situation the neighbour would be Bluemasters. Then:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian	Dane	Brit
pet		horse
drink	water	tea	milk	coffee	beer
cigars	Dunhill	Blends			Bluemasters

We still don’t know whether cats are on the left or on the right of Blends. Therefore, we have to keep the J part of JO:

B. Swede - dogs

F. birds - PallMall

J. (cats) | Blends | (cats)

M. German - Prince

Statement M can only apply to the fourth position, because it is the only one with both citizenship and cigars undefined. Then, the Swede of statement B can only be in fifth position:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian	Dane	Brit	German	Swede
pet		horse			dogs
drink	water	tea	milk	coffee	beer
cigars	Dunhill	Blends		Prince	Bluemasters

The two statements left are:

F. birds - PallMall

J. (cats) | Blends | (cats)

PallMall of condition F can only be in third position, which means that the Brit owns the birds. This resolves statement J because the only unknown pet neighbouring the Blends is in first position:

	1st	2nd	3rd	4th	5th
colour	yellow	blue	red	green	white
citizenship	Norwegian	Dane	Brit	German	Swede
pet	cats	horse	birds	fish	dogs
drink	water	tea	milk	coffee	beer
cigars	Dunhill	Blends	PallMall	Prince	Bluemasters

And it is the German who owns the fish!

I did waste some time at the beginning, before finding the right way of organising the information, but it took me 31 minutes to solve it. This is equivalent to an IQ percentile of 99.58, not inconsistent with what I had scored in the five IQ tests I had previously completed (from the most recent to the oldest: 99.96, 99.98, 99.82, 99.89, 99.87, 99.50).