Which of the following statements are true?

Which of the following statements are true? [ with your own reasoning, of course! ]

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.





Ans.
1,8,10,11,12

Logic:

1 is anyways true.
Assume that 12 is true.So we are left with 3 more statements from 2 to 11 which can be true.
We put 10 as true which makes 11 true, 12 is already true(we have assumed).If 11 is true then either 7,8,9 should be true. Only 8 satisfies the condition.