Did Sauron hold the 7 and the 9?

Question

In The Lord of the Rings Galadriel refers to Sauron as the holder of the 7 and the 9. But it also says in the appendices that dragons had consumed some. Is there a definitive answer to this discrepancy?

Yet even so, as Ring-bearer and as one that has borne it on finger and seen that which is hidden, your sight is grown keener. You have perceived my thought more clearly than many that are accounted wise. You saw the Eye of him that holds the Seven and the Nine. And did you not see and recognize the ring upon my finger? Did you see my ring?
-The Lord of the Rings, The Fellowship of the Ring, Book II, Chapter 7: "The Mirror of Galadriel"

Answer 1

When Galadriel calls Sauron "him who holds the Seven and the Nine", I would say we're supposed to read that phrase as if she's giving him an ad-hoc title. She's not really claiming that Sauron literally has possession of 16 rings of power, because I can't imagine she would not know better.

Using the same quotes that @Matt Gutting uses, we can see Gandalf also speaks of "The Nine" and "The Seven" as if they were proper nouns

Seven the Dwarf-kings possessed, but three [Sauron] has recovered, and the others the dragons have consumed. ... So it is now: the Nine he has gathered to himself; the Seven also, or else they are destroyed.

(The Fellowship of the Ring, Book I, Chapter 2, "The Shadow of the Past")

Note that Gandalf does not say "the Nine he has gather to himself; and also what remains of the Seven", or anything like that. He says "the Nine [...]; the Seven also", before adding on the qualifier that some of them have been destroyed. He uses those terms as names for the set of rings given to men, and the set of rings given to dwarves.

Tolkien's use of capitalization is also a common literary technique to indicate that the word is more significant than its normal meaning would imply, and he's consistent about doing so:

The Nine the Nazgûl keep. The Seven are taken or destroyed.

(The Fellowship of the Ring, Book II, Chapter 2, "The Council of Elrond")

You saw the Eye of him that holds the Seven and the Nine

(The Fellowship of the Ring, Book II, Chapter 7: "The Mirror of Galadriel")

Taken as a whole, this seems to indicate that, among those who were "in the know" about the Rings of Power, they used the terms "the Seven" and "the Nine" to simply refer to the entire set, however many happened to still exist, of those rings. So, when she says Sauron is the holder of the Seven, she just means possesses all the remaining dwarf rings.

Answer 2

Galadriel may be speaking more generally here; Gandalf says several times that some of the Seven have been destroyed:

Seven the Dwarf-kings possessed, but three [Sauron] has recovered, and the others the dragons have consumed. ... So it is now: the Nine he has gathered to himself; the Seven also, or else they are destroyed.

(The Fellowship of the Ring, Book I, Chapter 2, "The Shadow of the Past")

The Nine the Nazgûl keep. The Seven are taken or destroyed.

(The Fellowship of the Ring, Book II, Chapter 2, "The Council of Elrond")

It is certainly possible that Galadriel is unaware that four of the Seven were destroyed; but she seems to make a point of knowing what is going on in the world, and I deem this unlikely. More probably, I think, she is speaking in large terms, deliberately neglecting accuracy for the sake of brevity.

Answer 3

As early as chapter 2 in LOTR, The Shadow of the Past, Gandalf refers to the fact that Dragon-fire could consume the Great Rings. He subsequently refers to the fact that some of the Dwarf rings have in fact been destroyed by Dragon fire (which seems reasonable: we know from the earlier book, The Hobbit, that Dwarf gold attracts Dragons); so we presume that the reason why Gandalf knows that the Rings are vulnerable in this manner derives from the actual fate of some of the Seven Rings given to the dwarf-lords.

This is a very important plot point: Tolkien must establish from the outset, beyond doubt, that the One Ring can't be melted by just any passing dragon, such as Smaug in the earlier book. The validity of Frodo's quest to find the Fiery Mountain is dependent upon that being the only solution to the existence of the Ring. Gandalf is thus Tolkien's means of considering that possibility, and of explaining why it won't work.

In a sense, Sauron has "gathered to himself" the Nine and the Seven. So he has, possibly, sixteen rings to command. But we know that the One, which he has not, is the Ruling Ring: that all the others obey it. Tolkien never has Sauron sit down and work out a plan to siphon-off all the power of those sixteen, in order to build a new Ruling Ring: apparantly Elven Rings don't work that way. Nor do they have additive properties: Sauron can't overcome the One by weilding The Sixteen, on a 16-to-1 basis.

Actually, it is never even suggested that Sauron himself physically holds the Seven and the Nine. Possibly the Ringwraiths still bear the Nine, and part of their terror stems from their Ring, which Sauron had corrupted in the forging: the probability is that some part of his malignant nature must have passed into those rings, in order to bring them under his control.

Only a few of the Seven Rings of the Dwarves still exist; but these are useless to Sauron, because it has transpired that they do not in fact enslave dwarves. At one point, Sauron even offers to return these Rings, to the Dwarves of the Lonely Mountain, in return for news of the whereabouts of Bilbo and the One. The offer may not have been honoured, by Sauron the base master of treachery, but that he was willing to even make it says something about the uselessness of the Seven to him.