Given: X is an integer between 1 and 10, inclusive.

1.  X equals the sum of the statement numbers of the false statements in this
    list.
2.  X is less than the number of false statements in this list, and statement 10
    is true.
3.  There are exactly three true statements in this list, or statement 1 is
    false, but not both.
4.  The previous three statements are all false, or statement 9 is true, or
    both.
5.  Either X is odd, or statement 7 is true, but not both.
6.  Exactly two of the odd-numbered statements are false.
7.  X is the number of a true statement.
8.  The even-numbered statements are either all true or all false.
9.  X equals three times the statement number of the first true statement in
    this list, or statement 4 is false, or both.
10. X is even, or statement 6 is true, or both.

What is X?
And while you're at it, which statements are true or false?