A recent discovery of an as yet unpublished memo by the publisher Unwin, of Unwin, Wittering and Zigo, reports of an hitherto unsuspected encounter between Isaac Asimov and J.R.R.Tolkien in an hotel, where by pure chance, they were both attending international conferences by invitation. This would have been around 1949.
Asimov was of course well known for his biochemistry work at the nearby Columbia University, and was presenting his paper on "the melting point of benzoic acid and the feint possibility of room temperature superconductivity", whilst Tolkien was at the International Symposium of Runic Scholars, where he was going to speculate on "the possibility of artificial languages that could have their own symbolic script and may be a contribution to world peace".
Unwin reports that the two gentlemen collided in the elevator as they were coming down after breakfast to go to their respective events, both clutching, as it happens, draft early manuscripts of there soon to be famous major oeuvres, the preface to the Adventures of Susan Calvin, and There and Back Again, Again, Escape from Mirkwood. In the collision, both bundles of paper fell to the floor, and, unnoticed by their owners, were inextricably mixed.
Now we understand how it could happen that there were three laws that bound the behaviour of Hobbits, and that were seven rings for the mining robots, nine for the smart killer drones, three for the EVs, and one kept back for the POTUS. In a later story, Tolkien would revisit the three laws of Hobbits, and reason that Gandalf, an honorary Hobbit, perhaps was bound by a fourth (or more correctly, a zeroth) law, which subsumed all the others.
Asimov could never reconcile his Russian past with the idea that one human could possess such great power, and changed the end of the tale so that one ring was cast into the Yellowstone Caldera, and melted down, so that the three, seven and nine would now operate under true autonomy.
Fan contributed literature has tried to reconstruct the way the books might have been written without this terrible mashup, but little progress has been made coherently, partly because no-one has managed to find a convincing explanation of what happened to Susan Calvin. It has long been recognized that genre writers, even the very best like Asimov and Tolkien, were never much cop at character, least of all female characters. At least one partially successful attempt (you may have seen it adapted to Netflix) casts Gandalf as a woman (with a nod to Wilkie Collins' Woman in White).
To the end of their days, both authors insist that allegorical interpretations of their work are ill-founded, and they were just writing escapist nonsense. Religions have flourished on less.