The discovery by Ronnie B. Kon, which he reported in the Nov. 2010 Word Ways, of an earlier, different version of Faith Eckler's refractory "1831" riddle constitutes a breakthrough, I believe, in the decades-old effort to deduce a convincing answer to this stumper. Whereas before, this riddle had seemed (to me, at least) to be intractably baffling, now, suddenly, a satisactorily suasive solution to it is discernable.
"Resolving the Riddle: Plan Bee,"
Word Ways: Vol. 44
, Article 7.
Available at: http://digitalcommons.butler.edu/wordways/vol44/iss1/7