Persons of the dialogue:
Perictionè, Aristocles, Glaucon, Adeimantus, Socrates
Perictionè, the mother, and her three sons, Aristocles, Glaucon, Adeimantus, are conversing in their home in Athens.
Perictionè: Shortly before his death, my good husband Ariston, and your father, wrote a binding will spelling out what properties should be left to you, his sons. Being an exceptionally wise man, Ariston wrote in his will that he was dividing his estates between you in such a way as to insure that you, his sons, would find a truly initiated man to be your teacher and guide.
Along with the homestead which he deeded to me, your father left seventeen estates between you and decreed in his will that these properties should be divided among you in a very definite manner. None of the properties was to be sold before the division of properties was completed. Your father's will expressly stated that you, Aristocles, the oldest, should have half, Glaucon, the middle in age, one-third, and you, Adeimantus, the youngest, should have one-ninth.
However, since your father's death, we have invited over two dozen persons claiming to be advanced teachers and none of them has been able to divide the estates between you in the apportionment set out in your father's will.
Adeimantus: Perhaps we should sell the estates after all, and divide the sum of money in the fractions our father has set out.
Glaucon: No, our attorney tells us that this would invalidate the will.
Aristocles: The teachers you have invited, mother, though all possessing grand reputations, have all been sophists, as these are the most public teachers in Athens. Perhaps we should inquire of a teacher who is not a sophist.
Perictionè: Who do you suggest, Aristocles?
Aristocles: I have been studying for a short while with a teacher named Socrates, and I have asked him here today to see if he can solve the riddle of our father's bequest.
Perictionè: Excellent, I have heard that Socrates is a wise teacher. Perhaps he can find the solution to the enigma after all.
Socrates is announced by a servant and enters the room.
Perictionè: Welcome, Socrates. It is our fond hope that you can find a resolution to this conundrum. It appears that only a teacher who is also a magician can solve the enigma.
Socrates: I do not claim to be a magician, madame, but I will do my best. Tell me how your husband's will decreed that the apportionment of properties is to be made.
Perictionè tells Socrates of the details of Ariston's will.
Socrates muses for a few moments, then speaks to Aristocles.
Socrates: You have been studying with me for a short while, is that not true?
Aristocles: Yes, for just a little over two months.
Socrates: Do not your friends call you Plato, because you have a wide frame--and a broad turn of mind?
Aristocles (somewhat embarassed): Yes, they have given me that nickname.
Socrates: Then if you and your brothers will follow my way of thinking in this matter, I believe we can arrive at a solution to the problem of your father's bequest.
Everyone is excited by Socrates' statement.
Socrates: Glaucon, we will first add my own estate to the seventeen your father has left you three brothers. That will then make how many estates to be divided among you?
Glaucon: Eighteen in total.
Socrates (to Perictionè): Did your husband's will disallow the adding of an estate to the sum he left his sons?
Perictionè: No, there was no such stipulation.
Socrates: Now, Adeimantus, you were to receive what fraction of your father's estates?
Socrates: And one-ninth of eighteen is how many?
Socrates: And you, Glaucon, were to receive what fraction?
Socrates: And one-third of eighteen is what amount?
Socrates: Finally, you, Plato, were to receive what fraction of the estates?
Aristocles: Half, which is nine.
Socrates: Excellent. Then, Plato, what is the sum of 2, 6, and 9?
Socrates: And the one remaining, the eighteenth, I will reclaim as mine. And the enigma is solved.