Statements 6-10 cannot be true because they are all contradictions.

Statement 10 can never be true so it is always false which means statement 1 is always true

Statement 9 now can't be true because together with #1 there would be 2 true statements and 8 false statements. So #9 is always false. Now, that leaves statement #2 always true.

If Statement #8 were true, there would be 3 true statements so Statement 8 could never be true. Statement #8 is always false and makes statement #3 always true.

If Statement #7 were true, there would be 4 true statements so Statement 7 could never be true. Statement #7 is always false and makes statement #4 always true.

If Statement #6 were true, there would be 5 true statements so Statement 6 could never be true. Statement #6 is always false and makes statement #5 always true.

kweaver is correct.