Tolkien writes on page 59:
Yes, alas! through him [Gollum] the Enemy has learned that the One has been found again. He knows where Isildur fell. He knows where Gollum found this ring. He knows that it is a Great Ring, for it gave long life.
This implies that only the “Great Rings” give long life to a mortal, whether Man or Hobbit, not one of the lesser rings or some other ring-shaped charm. Earlier, on page 47, Gandalf refers to “the Great Rings, the Rings of Power”, as though they are synonyms for the same things. Now we are told that they alone give “long life”, for Gandalf makes the gift of “long life” evident proof that the Ring possessed by Sauron is one of the “Great Rings.”
But could Gollum’s Ring be one of the other nineteen “Great Rings” which also give long life? Gandalf indicates not. Tolkien makes Gandalf continue immediately following on the same page:
He [Sauron] knows that it is not one of the Three, for they have never been lost, and they endure no evil.
Also the Three, according the Waldman letter, “did not confer invisibility”. But Tolkien is not discussing such matters, only the ability of all the Great Rings and only the Great Rings to give long life.
Gandalf is made to continue:
He [Sauron] knows that it is not one of the Seven, or the Nine. for they are accounted for.
Gandalf has earlier explained on page 51:
Seven the Dwarf-kings possessed, but three he [Sauron] has recovered, and the others the dragons have consumed. Nine he gave to Mortal Men, proud and great, and so ensnared them.
So Gandalf now makes clear:
He [Sauron] knows that it [the Ring won from Gollum by Bilbo] is the One.
Yet Gandalf on page 55 declares of “A Ring of Power”, which is elsewhere in this chapter a synonym for “Great Ring”, has never in all history been freely given up by its keeper save when Bilbo gave up the Ring of Power he possessed to Frodo.
Hammond and Scull state:
This is true of the One Ring, but not of all Rings of Power, of which Gandalf seems to be speaking generally. Celebrimbor gave away the Three Rings. Círdan gave his Ring to Gandalf, Gil-galad (when dying) gave his to Elrond, and Thrór gave his Ring to Thráin.
I have restated the problem more clearly as I see it.
Zigûr’s attempted answer seems to me to depend on Gandalf using “Rings of Power” to refer only to Sauronic rings, which I don’t see on further study. And he does not account for Thrór giving up his Ring to Thráin. See #21 in the thread “The Effect of the Great Ring”.
Findegil answer in the thread “The Effect of the Great Ring” seems to me to merely accept that Gandalf is lying, but for good reasons. This works, but seems to go against Gandalf’s truthfulness elsewhere. See #30 in the thread “The Effect of the Great Ring”.
Inziladun’s explanation does not fit with Gandalf’s own explanation of the powers of the Rings.
Morthoron’s attempt at explanation I do not understand at all. He asks:
So why would Gandalf confuse Frodo with provisos, quid pro quos, caveat emptors and various other Latin phrases that may or may not have anything to do with what Gandalf was talking about and what he needed to impress upon Frodo so that the Hobbit could achieve his mission?
Gandalf doesn’t do this and no-one, certainly not me, thinks he should.
My own answer would be blamed by me for changing the text which many would call cheating. Very weak.