Ἑρμότιμος ἢ Περὶ Αἱρέσεων

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42–43

HERMOTIMUS

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.

LYCINUS

How, Hermotimus?

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. 5

LYCINUS

Shall I praise you for your intelligence, or would you like me to explain the different view I have of the matter?

HERMOTIMUS

Certainly. But I fail to see what reasonable answer you can give to such an argument.

LYCINUS

You have spoken as if the letters are definitely written in order—I mean alpha first, beta second, and so on through the alphabet, until the number of competitors is completed at one of them. I grant that this is so at Olympia. But suppose we choose five letters completely at random—chi, sigma, zeta, kappa, and theta—and we write four of these twice on eight lots, but the zeta only on the ninth, which is going to show us the bye. What will you do if you find the zeta first? How can you pick out the competitor who holds it as the man for the bye, without going to all the others and finding no letter to correspond to it? You cannot, as you were just now, be sure from the alphabetical order.

HERMOTIMUS

What you ask is difficult to answer.