The Scythian or Consul (42)

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.