Stop there. This is just what I wanted. Now, suppose they are nine in number and they have all drawn and are holding their lots. You go round (I want to make you a National Judge instead of a spectator) and inspect the letters. I fancy you will not learn in advance who has been given a bye, unless you go to every one of them and pair them.
What do you mean by this, Lycinus?
It is impossible immediately to find that letter which gives you the bye, or perhaps you could find the letter, but you will certainly not know if it is that one, for there is no prior declaration of kappa or mu or iota as the letter which chooses the bye. When you find alpha, you look for the competitor who has the other alpha, and, when you find him, you have already paired them. Then again, when you come on beta, you look for the other beta, the counterpart of the one you have found, and so with all of them, until you are left with the competitor who has the only letter that has no counterpart.
What if you come on this one first or second, what will you do?
It is not what I shall do. You are the National Judge, and I want to know what you will do. Will you say at once that this man is given a bye, or will you have to go round them all, to see whether there is somewhere a corresponding letter? If you did not look at the lots of everyone, you would not discover who had the bye.
Oh, I should know quite easily, Lycinus. In the case of nine competitors, if I find epsilon first or second, I know that the one holding this lot is the one who has the bye.
How, Hermotimus?
In this way: two have alpha, and similarly two have beta. Of the remaining four, two have surely drawn gamma and two delta, and four letters have already been used up for eight competitors. So it is clear that only the next letter, epsilon, could be odd, and he who has drawn this one gets the bye.
Shall I praise you for your intelligence, or would you like me to explain the different view I have of the matter?
Certainly. But I fail to see what reasonable answer you can give to such an argument.