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How Many El's in a Zod?

OK, the debate goes on.
One of the continuing mysteries of Diablo II is "How many El's are there in a Zod?"
Admit it, you stay awake some nights, wondering about it, don't ya?
Oh, please. I know you do!

So I was originally told that there are "1,144,561,273,430,840,000,000,000,000,000 El runes in a Zod rune".

Richard wrote in to tell me that this number is about a billion-billion times too large. He said that the correct formula is as follows:
1 Eld = 3 El (or 1 * (3 to-the-power of 1))
1 Tir = 9 El (or 1 * (3 to-the-power of 2))
1 Nef = 27 El (or 1 * (3 to-the-power of 3))
This means to get to a single Pul rune you need 3,486,784,401 (or 1 * (3 to-the-power of 20)) El. From there you need two of each rune, up to Zod.
1 Um = 6,973,568,802 El (or 3,486,784,401 * (2 to-the-power of 1))
1 Mal = 13,947,137,604 El (or 3,486,784,401 * (2 to-the-power of 2))
1 Gul = 27,894,275,208 El (or 3,486,784,401 * (2 to-the-power of 3))
Bottom line, this means to get to a Zod rune you need 14,281,868,906,496 (or 3,486,784,401 * (2 to-the-power of 12)) El (plus assorted chipped to flawless gems).

Andrew wrote in to say that he got a different number. The way that it was figured it out, was by raising 3 to the power of whatever rune you wanted to find. (3 to the power of one for an Eld, 3 to the power of 2 for Tir...etc) So he counted all of the runes, and including the El, there are 33 of them. Therefore, to find how many El's there are in a Zod, you raise 3 to the power of 32. When he did this, this is the number that he got: 1,853,020,188,851,841.

James, who not only plays DII, but also contemplates the number of El's in a Zod, while supervising race tracks in the desert (talk about multi-tasking!!), says that Richard is wrong, and that although Andrew's formula is correct, his final answer is wrong. The correct calculation would be 3 to the 32nd power, which comes out to be: 1,853,929,019,000,000. That's a heck of a lot of El runes, if you ask me.

Nick H says that it's:
3^20 = 3,486,784,401
(there are 20 runes that you need 3 of each to make the next rune)
then multiply that number by 2^12
(there are 12 runes that you need 2 of each to make the next rune)
So his total is 14,281,868, 906, 496

Joe T pointed out that Andrew and James are wrong, because you need 3 of each rune from El to Pul, and then 2 of each run from Pul to Zod. Which is also what Nick said.

Brian T says that it's:
3^32, if you are talking about DII v1.09
(3^20)*(2^12), if you are talking about DII v1.10 or higher

Maggie Z says that she got 1,853,020,188,851,841, but gave no indication of how she arrived at that number.

Andrew P says it's:
(3^20)*(2^12), which equals 14,281,868,906,496

Fritz agrees with Richard, Nick, Joe and Andrew, and has advised me that he is moving on to determine the number of licks it takes to get to the center of a Tootsie-Pop!

To tell you the truth, I simply don't know; math was never my strong subject.

I would like to take this opportunity to thank everyone who has taken the time to figure this out. Now quit wasting time playing math games, and get back to playing DII!!!!

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