The puzzle of the five discs

“When Princess Dahize was eighteen years and twenty-seven days old, her hand in marriage was sought by three princes whose names have passed into legend: Aradin, Benefir, and Comozan.

“King Cassim was uncertain. Of the three rich suitors, how could he choose the one who should marry his daughter? If he were to do so, it could have the following fatal result: he, the king, would gain a son-in-law, but the two unsuccessful suitors would become his bitter enemies. It was a hard decision for a sensitive and cautious king who only wanted to live in peace with his people and his neighbors. He asked Princess Dahize, but she declared only that she would marry the one who was most intelligent.

“Her decision pleased King Cassim, for he saw a simple solution to what seemed an impossible choice. He summoned five of the wisest men in his court and told them to put the three princes through a rigorous test to see which of the three was the most intelligent.

“When they had done so, the wise men reported to the king that all three princes were indeed most intelligent. They were well versed in mathematics, literature, astronomy, and physics. They could solve difficult chess problems, the subtleties of geometry, and all kinds of complex enigmas. ‘We do “not see any way,’ said the wise men; “of making” a clear decision in favor of one of them.

“After this distressing failure, the king decided to consult a dervish who had a reputation for knowing much about magic and the occult.

“The dervish addressed himself to the king. ‘I know only one way that will allow us to decide which prince is the most intelligent of the three—the test of the five disks.’

“‘Then let us do it!” exclaimed the king.

“The three princes were summoned to the palace, and the dervish, showing them five simple wooden disks, said to them, ‘Here are five disks, two of them black and three of them white. They are all the same size and weight and are different only in color.’

“Next, a page carefully bound the eyes of the three princes so that they could-see nothing. The old dervish then picked three disks at random and fastened one each to the backs of the three suitors, saying as he did so, ‘Each one of you has on his back a disk whose color you do not know. You are to be questioned in turn. The one who discovers the color of the disk he is wearing will be declared the winner and will receive the hand of the beautiful Dahize in marriage. The first one questioned can look at the disks of the other two. The second can see only the disk of the third, and the third must make his reply seeing none of the others. The one who gives the correct answer must, in order to prove that he was not simply guessing, justify his answer by clear reasoning. Now, who wants to go first?’

“‘Let me be first,’ said Prince Comozan promptly.

“The page removed the bandage from his eyes, and Prince Comozan saw the disks on the backs of his two rivals. The dervish took him aside to hear his answer, but it was wrong. Declaring himself beaten, he withdrew. He had seen the two disks on the hacks of the other princes and still not been able to determine the color of his own disk.

“‘Prince Comozan has failed,’ said the king in a loud voice, to inform the other two.

“Then let me be next,’ said Prince Benefir. Once his eyes were uncovered, the second prince saw the disk worn by the third on his back. He motioned to the dervish and whispered his reply to him. The dervish shook his head. The second prince was also mistaken and was given leave to withdraw immediately. Only one was left, Prince Aradin.

“When the kin” announced that-the second suitor had also failed, he approached with his eyes still bandaged and announced in a loud voice the correct color of the disk on his back.”

When the story was finished, the wise man pf Cordoba turned to Beremiz and said, “In making his answer. Prince Aradin reasoned in such a way as to reach with complete certainty the solution to the problem of the five disks and to win the hand of the beautiful Dahize. Now, I wish you to tell me, first, what his reply was and, second, how he could be so “sure of the color of his own disk.”

A Collection of Mathematical Adventures
by Malba Tahan
Chapter 31: IN BLACK AND WHITE
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