An ancient riddle tells of three wise men from three different
empires who showed up one day at the gate to a peaceful kingdom. Each
had come to seek asylum from the horrible three-way war that had
brought their empires to ruin.
The queen of the peaceful
kingdom arrested the three wise men and brought them in chains before
an assembly of her people. With all the citizens present, she asked the
three wise men why, if they were so wise, they had not been able to
prevent their kingdoms from destryoing each other.
"The people
of each empire, against the advice of their wise men and their
emperors, willed that the other empires be destroyed; the emperors had
no choice but to comply." said the first wise man.
"The
emperors of each empire, against the advice of their wise men and their
people, willed that the other empires be destroyed; the people had no
choice but to comply," said the second.
"The wise men of each
empire convinced the emperors and the people, against their better
judgment, willed that the other empires must be destroyed; the emperors
and the people lacked the wisdom not to comply," said the third.
The
queen spoke: "No one shall be a wise man in my kingdom who does not
know why kingdoms collapse. So I ask you three wise men, former
enemies, to confer among yourselves and decide which answer is correct.
If you cannot reach agreement on that, none of you is fit to be a wise
man in my kingdom."
The three wise men conferred for several minutes. Then one of them said, "All three answers are correct, your highness."
"You
are wise indeed," said the Queen, "but I have no place in my kingdom
for three clever enemies who might destroy my people the way you have
destroyed your own.
Only one of you can stay."
She
continued, "The rules are simple. I will ask you to solve a riddle that
none of my subjects has been able to solve. The one who solves it first
will be allowed to stay and will live as the wisest man in my peaceful
kingdom."
The Queen then blindfolded the three wise men, and
she painted a dot on the forehead of each. She asked her citizens to
take note of the color of each dot, but to keep silent about it. The
citizens could see that the color of each dot was red.
The
Queen then took off the blindfolds and had the three wise men face each
other. "I have painted either a green dot or a red dot on your
foreheads," she said. "Raise your right hand if you see a red dot on at
least one of the foreheads facing you."
Each wise man raised his hand.
"Now,"
ordered the Queen, "without talking, and using only information
provided, you must figure out the color of the dot on your own
forehead. The first to do this will be allowed to stay in my peaceful
kingdom."
The first wise man thought, "The other two have
raised their hands. Therefore, each of them sees a red dot. I can see
that they both have red dots on their own foreheads. But they would
both raise their hand whether the dot on my forehead was red or green.
So there is no way for me to know whether the dot on my forehead is red
or green."
The second wise man thought, "This riddle is
unsolvable. If the dot on my forehead is green, I would see what I am
now seeing: the other two with their hands raised, and me with my hand
raised. If the dot on my forehead is red, I would also see what I am
now seeing: the other two with their hands raised, and me with my hand
raised. Because the only information I have to go on is the observation
that all three hands are raised, and all three hands would be raised
whether the dot on my own forehead is red or green, I have no way of
determining whether my dot is red or green."
Ten minutes passed. Suddenly, the third wise man exalimed, "The dot on my forehead is red!"
How did he know?
