Which of the following statements is true?

1. Exactly one of these ten statements is false.

2. Exactly two of these ten statements are false.

3. Exactly three of these ten statements are false.

4. Exactly four of these ten statements are false.

5. Exactly five of these ten statements are false.

6. Exactly six of these ten statements are false.

7. Exactly seven of these ten statements are false.

8. Exactly eight of these ten statements are false.

9. Exactly nine of these ten statements are false.

10. Exactly ten of these ten statements are false.

Which of the above statements will be true and which of them will be false, if you remove the word 'Exactly' from all the statements ?

(In reply to

Still Doesnt Make Sense by Lucifer)

in the example you have provided Lucifer, you are saying that if the statement contains the word Pie and something like that which might lead you to a paradox but in the given problem, i think one or more statement depends on the truth and falsity of the other statements as each statement is not independent of the rest of the statements.

It is just like Cory has mentioned in his proof that a statement’s value of true forces all lower numbered statement to have a value of true and conversely a false statement forces all higher number statements to be false. Now you can use these facts and consider all the other possibilities which can give you a correct result instead of considering the wrong statement and arriving at a paradox.