Puzzle Redux

I don't mind re-running posts or puzzles that I've posted before that are personal or reader favorites, so below is one from almost 3 years ago that still gets hits each month. (It's the sort of puzzle that Rick Kurshen just might love. ;-))
I'd already seen it multiple times on the Web when I first ran it (though I don't know where it originated???), so I realize many of you have seen it already, but if not, give your brain a whack at it, if you dare!

[The general consensus from those who have coded the problem and run it, is that there is one lone correct answer, which I'll eventually insert in comments if no one else does.]

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Given the following 12 statements which of the statements below are true?

1.  This is a numbered list of twelve statements.
2.  Exactly 3 of the last 6 statements are true.
3.  Exactly 2 of the even-numbered statements are true.
4.  If statement 5 is true, then statements 6 and 7 are both true.
5.  The 3 preceding statements are all false.
6.  Exactly 4 of the odd-numbered statements are true.
7.  Either statement 2 or 3 is true, but not both.
8.  If statement 7 is true, then 5 and 6 are both true.
9.  Exactly 3 of the first 6 statements are true.
10.  The next two statements are both true.
11.  Exactly 1 of statements 7, 8 and 9 are true.
12.  Exactly 4 of the preceding statements are true.

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