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 ?

without the word exactly included, if a statement is true, then so are all preceeding statements (if 3 are false, then AT LEAST 2 are false etc.), so this boils down to only 10 situations - which is the highest numbered true statement? Using my favorite analytical method (brute force), the first five statements are true, and 6 through ten are false.
btw, if not obvious, when the "exactly" is included, there is only one true statement, and it's #9.

Or I could be wrong...

Posted by Cory Taylor on 2003-02-25 08:28:42