LotR -- Book 6 - Chapter 4 - The Field of Cormallen

[Child of the 7th Age]

Where did these sayings originate? And why, exactly, does the third time pay for all?

Regarding why the third time pays for all....

"Three" has a special meaning in fairy tales. For example, the hero is usually given three trials. He fails the first two and succeeds at the third. Thus, "three" is the path of wisdom. The number three is found in so many tales, and the third person or try often represents wisdom:

• 3 billy goats gruff: it is the third goat who bests the troll
• Goldilocks and the 3 bears--it is the third and littlest bear who finds Goldilocks
• 3 little pigs -- it's the third pig whose house prevails
• 3 sisters in the Cinderella story and the third daughter is "blessed" with looks and wisdom
• 3 sons in Puss in Boots and, of course, it's the third one who shows his wisdom by getting the cat

There are also three Graces (Greece), three Norns (past, present, future) of Norse myth, and, of course, the Trinity, all of these representing enlightenment. I known that some point to the mother/father/child triad as the origin of this usage with the child pointing to the path of wisdom.

I think Tolkien is using three in its traditional sense, as a tip of the hat to the Gaffer's experience or wisdom, which his son acknowleges. I do know you can google the phrase "third time pays for all" and come up with several modern instances of the phrase. But as to how this specific saying originates in the context of Middle-earth (or of our earth), I am not sure at all.

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P.S. I didn't see your edit till now. Very interesting. Notice also the use of three times three.