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The way i see it. To be fare to all the players who turn out to there div.
singles is to have a open draw on the day. Allocate each player a number when they sign-in. Add that number to the draw-bag. put the number of byes needed to make a 1st round line-up in a separate bag make the draw at 12o/clock in front of all the players present .
you start the draw with the first bye then a player then a bye and so on until all the byes have gone and continue with the players only to finish the draw for the 1st round .