Dorfman's Group Testing

The estimable Xi'an's OG https://xianblog.wordpress.com/2020/04/09/dorfmans-group-testing/has recently pointed out that the group testing idea that has been recently put forward for Covid-19 appears as Problem IX.9.26 in Feller attributed to the late Robert Dorfman.  This problem is notable for being one of the easier problems in Feller, suitable for a serious undergraduate course and particularly apt in the present circumstances.  Dorfman's application was testing GI's for syphilis before sending them abroad into WWII.  Since I have already besmirched the reputation of Dorfman in a previous post https://davoidofmeaning.blogspot.com/search?q=dorfman it seems only fair that I recant a bit and acknowledge that this group testing idea was really quite clever and practically quite important.  I won't spoil the problem by revealing the answer, but I'll provide a snapshot of it here for those unlucky enough not to have a copy of Feller handy.  (Mine has been inherited by a terrific ex grad student who was kind enough to send me a scan.)