An alternative
solution to the blue eyes riddle
This is the second article that I have decided to write
about how to solve some of the most difficult logic puzzles in the world by
using interpretations that are slightly different to that of the accepted
official versions. In the first article I presented an alternative solution to
George Boolos’ “Three Gods riddle” which has been described as the hardest
logic puzzle in the world. In this second article I will present an alternative
solution to the ‘Blue eyes riddle’ which has been described in similar terms. I’m
not going to spend any time examining the truthfulness of such claims; I’ll
leave that up for the readers to decide for themselves. I will mention however that
it took me quite a while to finally come up with a viable solution, and odds
are that most people who decide to try and solve this puzzle will have similar
experiences.
Like I mentioned, this is an alternative solution to the
accepted ‘official’ solution which can be found on various websites. That
however doesn’t mean that the solution presented here is wrong or that the official
solution is somehow better or worse, it just means that when it comes to logic
puzzle and riddles there are often more than just one solution. This is largely
due to the fact that riddles and puzzles, given their ambiguous nature are open
to interpretation. It should be obvious to everyone that logic puzzles are very
different to mathematical equations that only come with one correct answer. It’s
an indisputable fact that 2 + 2 = 4; it’s however not a disputable fact that
riddles can be solved by using methods other than complex mathematical calculations.
It is important to remember that any riddle should be interpreted
based on the actual wording of the riddle, and not on what the creator had in
mind when he or she wrote it. It is the responsibility of the creator to ensure
that the wording is as accurate as humanly possible in order to eliminate
alternative interpretations that subsequently leads to alternative solutions.
That however isn’t always the case and hence many riddles have more than one
solution. To be fair it is difficult to prevent such outcomes, riddles and
logic puzzles would have to contain extremely long unambiguous texts and long
and detailed explanations in order to eliminate such misunderstandings, a fact
I guess that many a riddle maker can attest to when people start questioning
the ‘official’ answer that he or she had intended for it.
The alternative solution along with a detailed explanation
as to why this is an acceptable solution can be found below this paragraph.
Those who wish to try and solve the riddle themselves should refrain from
reading any further, that is unless they wish to find out the alternative and
the official solution. It should be noted that this is a valid solution based
on the criteria set out in the riddle, and that it doesn’t violate any of the
criteria relied upon in the official solution.
This particular solution, along with the official one hinges
on the fact that the logicians weren’t somehow able to come up with a foolproof
method of determining their own eye colour on the first day and thus were able
to leave the island. I think it is safe to conclude that they didn’t as there
were people present on the island when the Guru made her announcement.
The solution
One of the most difficult aspects of any logic puzzle or
riddle is to identify what is important and what isn’t. Sometimes a riddle can
contain an overwhelming amount of information and it can be challenging to
separate the important bits from the trivial and more unimportant bits. That is
also the case with this particular riddle. The reader is presented with a wide
array of information that could or could not be significant. For instance we
are told that the ferry arrives every day at midnight to collect the islanders
who have successfully guessed their own eye colour. Is this an important aspect
of the puzzle? No it isn’t. The riddle would still be the same if the ferry
arrived at three o’clock in the afternoon or ten in the evening.
Is the fact that the Guru has green eyes an important aspect
of the riddle? No, and nor is the fact that she is a woman. Furthermore, the
fact that they are on an island is also unessential, they could just as easily
have been in a secluded area on the mainland. The most important piece of
information presented in the puzzle, and the information which will eventually
help us solve it is the statement made by the Guru; “I can see someone who has
blue eyes”.
So why is this the most important piece of information? It’s
the most important piece because that’s what all our logical conclusions are
based upon. The statement is the tool that will help us solve the riddle, it
would in all likelihood be impossible to solve it without it.
Upon hearing the Guru, who is facing the islanders while
uttering the words; “I can see someone who has blue eyes” the islanders who are
all super smart logicians immediately realise that all the blue eyed persons
have been given a free one-way ticket off the island. One can also safely
conclude that the Guru has come to the same conclusion as she should, at least
in theory, be even smarter than her fellow islanders and thus be more capable of
making such logical deductions.
This is how the
islanders utilize the statement to their advantage in this alternative
solution;
After having listened to the Guru utter the words the
islanders immediately look at the person standing next to them to check this person’s
eye colour. If the person happens to have blue eyes, the logician who first
turned his gaze will leisurely walk in front of this blue eyed person with his
face turned towards him, and in effect copying the behaviour of the Guru who only
seconds ago uttered the words “I can see someone who has blue eyes”. This behaviour
will then be copied by all the other islanders, and they will all understand
the significance of it.
So what happens with the brown eyed islanders?
In the case where the person who has just positioned him or
herself in front of a blue eyed person happens to have brown eyes, the blue
eyed logician will choose to remain where he or she is and refrain from walking
around to the other side to look at the person facing them. If the blue eyed logician
does walk around to the other side, the other person will then turn around to
confirm that he or she is one of the lucky ones, namely that he or she has blue
eyes and subsequently can leave the island at midnight.
Thus all the blue eyed persons on the island will have
established in a very short time that they have indeed blue eyes and that all
of them have earned themselves a one way ticket off the island. The brown eyed
people however aren’t that fortunate and they will have to remain on the island
indefinitely. They will have to do so because no one has uttered the words that
they can avail themselves of to convey to the remaining 100 people on the island
that they have brown eyes, namely; “I can see someone who has brown eyes”.
Some will probably protest after having read these last
paragraphs and maintain that the people on the island simply wouldn’t grasp the
significance of the act of positioning oneself in front of a blue eyed person,
but I would disagree. I understood the significance of it, thus it stands to
reason that the smartest logicians in the world would also understand the
significance of it. It should also be added that the islanders have spent a
long time on the island trying to figure out this exact question, so when
someone finally offer them a clue they should be expected to pounce on it.
I guess an equivalent scenario would be some friends watching
a comedy act on TV, and upon hearing the comedian says: “I’m now standing in
front of an idiot!” one of the friends would get up from his seat and positions
himself in front of another one with a big grin on his face, looking to elicit
a cheap laugh from the others. It should also be noted that people that are a
lot less smart than your average logician would get the meaning of such a
gesture, thus it stands to reason that the logicians on the island would get
the meaning of it too.
Some of those who read this alternative solution will
protest vehemently and maintain that the behaviour exhibited by the logicians
in the preceding paragraphs are unacceptable as it constitutes some form of
signalling or other unacceptable behaviour based on the criteria stated in the
riddle. So do they have a valid point, or are their protestations devoid of
substance?
Well if we read the riddle one more time and go through it
more methodically, we’ll see that it states that the islanders are not allowed
to communicate with each other, nor that they can invent any type of sign
language with the aim of revealing the colour of their fellow islanders’ eyes.
So once again, as is the case with so many other riddles, it comes down to
interpretations. However before we start analysing the no-no’s let’s have a quick
look at what the islanders are most definitely allowed to do according to the
riddle.
We know that the islanders are allowed to look each other in
the eyes, and we know that they are allowed to keep precise records (mental
records?) of the other inhabitants’ eye colours. We also know that they are
allowed to walk around freely as there is nothing in the riddle banning them
from doing so, it’s also worth noting that according to the official solution the
islanders can go down to the water during midnight to see if anyone is leaving
the island on the mysterious ferry that appears every day at midnight. We can
also conclude that they are allowed to walk around freely based upon the
knowledge that the Guru addressed them at noon on one specific day during their
endless stay at the island, and the fact that they were facing her when she made
her statement.
Next we need to figure out what constitutes communication. What
behaviour needs to be present in order for us to conclude that communication
between two or more individuals have taken place? It is not unreasonable to
maintain that communication involves some of the following actions; speech, utterance
of sounds, some sort of sign language, arm movement, eye movements or moving of
other parts of the body with the specific aim of conveying some type of message.
I would maintain that positioning oneself in front of another person and
looking at this person without doing any of the aforementioned activities does
not constitute communication. As a matter of fact such interpretations would
mean that the islanders would be communicating with each other every time they
looked each other in the eyes in order to keep record of the various types of eye
colours. Such interpretations would in
fact make the riddle unsolvable and render the official solution completely
useless, and besides there is nothing in the riddle that explicitly prohibits
any of the islanders from positioning themselves in front of their fellow islanders
while looking them in the eyes.
Furthermore in the official solution the islanders rely on
observations made at the docking site of the ferry to determine whether they themselves
are blue eyed or not, and thus in effect they are relying on the deliberate
actions of others, i.e. other islanders premeditated absence from the area in
order to establish their own eye colour. In the most extreme and rigid
interpretations of this riddle, this could then be construed as signalling or
as a form of secret communication, but it isn’t. Nor does the riddle forbid the
islanders from doing so. Thus the only logical conclusion that we can draw from
this is that the alternative solution that has been presented in this article
has to be considered valid, as it doesn’t involve the islanders relying on any
form of banned communication in order to reveal the eye colour of their fellow
islanders.
And voila, we have established that this solution is on par
with the official one. It’s also a much easier solution than the official one as
it doesn’t rely on convoluted logic. In my opinion it’s a perfect example of
Occam’s razor in practice; it relies on fewer logical conclusions to reach a sound
rational
solution.
