If you were following the discussion about ambiguity in elided phrases here, or even if you weren’t, let me highly recommend the book that is discussed there: Indices and Identity by Robert Fiengo and Robert May. It turns out the problem I half stumbled on is much harder than I realised, and they do a very good job of setting the problem out clearly, showing how it relates to other problems, showing that none of the (very many) pre-1994 solutions work, and then setting out an interesting solution of their own. I now have to figure out whether I agree with their solution, but that probably invovles reading all of the book, not just the sections on this puzzle.