True statements are underlined. BTW it wasn't hard at all just little use of logic, but definitely not hard.
I did solution with Dirichlet's box principe (aka Pigeonhole principe).
Which of the following statements are true?
1. At least one of these ten statements is false.
2. At least two of these ten statements are false.
3. At least three of these ten statements are false.
4. At least four of these ten statements are false.
5. At least five of these ten statements are false.
6. At least six of these ten statements are false.
7. At least seven of these ten statements are false.
8. At least eight of these ten statements are false.
9. At least nine of these ten statements are false.
10. At least ten of these ten statements are false.
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