How many of them are true?

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Lies, Almost All Lies Here are ten numbered statements. How many of them are true?
1. Exactly one of these statements is false.
2. Exactly two of these statements are false.
3. Exactly three of these statements are false.
4. Exactly four of these statements are false.
5. Exactly five of these statements are false.
6. Exactly six of these statements are false.
7. Exactly seven of these statements are false.
8. Exactly eight of these statements are false.
9. Exactly nine of these statements are false.
10. Exactly ten of these statements are false.

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All the statements contradict one another, and therefore at most one of them can be true, in which case the other nine statements will be false, which is what statement nine asserts.
Therefore statement nine is the only true statement.

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