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).