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.