Below are ten statements concerning X, a whole number between 1 and 10
(inclusive).  Not all of the statements are true, but not all of them
are false either.  What number is X?

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.