A Ruler in Persia

Question:

Once upon a time there was a ruler in Persia who had a very beautiful daughter. When it was time for her to be married, the marriage was arranged by her father as was the custom in that part of the world. Many young men came to be interviewed by the ruler, but no one person was perfect for the princess. After several months, the ruler finally decided that three princes from nearby kingdoms were suitable for the princess. Since each one was equal to the other in wealth, personality, manners, looks and intelligence, the princess’s father had to devise a way to differentiate between them and declare one as the man who would marry his daughter.

He invited the three of them to his palace and brought them to a room, elegantly furnished and with a single round table about 2 meters in diameter. There were three chairs around the table, equally spaced from each other. He bade them each take a seat. By this time, the three princes were puzzled by the secretive behavior of the ruler, (and I don’t mind telling you), a little apprehensive. But the ruler smiled and proceeded to explain to them that he considered each of them to be equally qualified to marry his daughter, so he had created a game to determine which one would win the hand of his daughter.

He produced three elegant scarves, woven of the finest silk and blindfolded each prince with them. Then he proceeded to explain that he had in his hand a contained of lampblack. This was a very common ingredient of the day, as it was used to make a sort of ink. But in its dry form, it could be used to make a mark similar to chalk. He approached each man and with his forefinger, made a mark of “X” on each mans forehead. As he explained to them, he MAY or MAY NOT have lampblack on his finger as he made each mark. Thus, each man could have a black “X” on his forehead or could have no visible mark at all. But he told them also that one or more of them had a black mark.

Now, said the ruler, take off your blindfolds. As each man did and became accustomed to the light, the ruler said, “The first man who can correctly tell me whether he has a black mark or not will be the man who will marry my daughter, the princess. You may not touch yourself or each other or move from your chairs.”

Seeing that neither he nor the other two had an immediate response, after a short time, one of the men stood up and correctly stated how his forehead was marked, and, was declared the winner. For your information, all three men were marked with black “Xs”.

How did the winner determine he was marked with a black “X” rather than no “X”?

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Solution: The reason he deduced he had one was that basically, he was the first to realize this;
Let’s call him A and the losers B and C.
IF B and C didn’t have x’s, then A would know right away because at least one person has one.
IF B had one and C didn’t then A would also know that He has one because B would have come to the same conclusion (i.e. A and C don’t have one so I must)
Knowing these two facts and knowing that both B and C would have figured these two facts out as well since there was no response, then A naturally deduces that He Must have an X as well.
Had nothing …absolutely nothing with them trying to trick him.

 

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