The Scythian or Consul (43)

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.

What you ask is difficult to answer.