The three wisest sages in the land were brought before
the king to see which of them were worthy to become the
king's advisor. After passing many tests of cunning and
invention, they were pitted against each other in a
final battle of the wits.
Led blind-folded into a small room, the sages were
seated around a small wooden table as the king described
the test for them.
"Upon each of your heads I have placed a hat. Now you
are either wearing a blue hat or a white hat. All I will
tell you is this- at least one of you is wearing a blue
hat. There may be only one blue hat and two white hats,
there may be two blue hats and one white hat, or there
may be three blue hats. But you may be certain that
there are not three white hats."
"I will shortly remove your blind folds, and the test
will begin. The first to correctly announce the colour
of his hat shall be my advisor. Be warned however, he
who guesses wrongly shall be beheaded. If not one of you
answers within the hour, you will be sent home and I
will seek elsewhere for wisdom."
With that, the king uncovered the sages' eyes and sat in
the corner and waited. One sage looked around and saw
that his competitors each were wearing blue hats. From
the look in their eyes he could see their thoughts were
the same as his, "What is the colour of my hat?"
For what seemed like hours no one spoke. Finally he
stood up and said, "The colour of the hat I am wearing
is . . ."
Answer to the
riddle . . . .
The answer is:
The hat is
At first glance, this problem appears to be impossible
to solve. Contributing to this is the feeling that the
King's only real clue - that there is at least one blue
hat - is useless since the sage can clearly see that
there are at least two blue hats.
Don't feel bad if you sat stuck on this one for a while:
as the puzzle clearly states, so did the three wisest
sages in the kingdom. It is this fact that allowed our
sage to give his answer. In truth, any one of them would
have come up with it, given enough time. Why?
Consider a situation which we knew was not the case-
that there was exactly one blue hat. What would happen?
There would be a split second of pondering by the person
wearing that hat, and he would say "I am wearing a blue
hat." No real puzzle there, but of course there wasn't
just one blue hat. The important fact is that everyone
knew there was not one blue hat. But more importantly
than that, everyone knew, or could quickly figure out
that everyone else knew this (by the fact that answer
was did not come out in the first few seconds.)
This leaves everyone wondering, "Are there two or three
Consider this less obvious situation- that there were
exactly two blue hats. This seems a very real
possibility at first, after all, we can see exactly two
blue hats. So everyone sits and thinks- for a little
while. But if there are only two hats, then two people
see one blue and one white hat. These two people will
very quickly, by virtue of the other's silence, rule out
the possibility that there is only one blue hat. One of
these two lucky sages would cry blue within a few short
minutes, if that long.
There is only one case which forces the three sages to
sit in silence - three blue hats. Our sage, through his
sharp wits was the first to reach this conclusion.
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