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 ?

All of the statements disagree, so only one can be true. This means that statement 9 must be true, because if 1 is true 9 are false.

If the word exactly is removed 10 can't be true, because that would be a contradiction. That means statement 1 is definitely true.

That also means statement 9 can't be true, because that will also be a contradiction. Using this logic we can tell that statements 6,7,8,9 & 10 are all false, so 1,2,3,4 & 5 are true.

Posted by Lewis on 2003-06-14 00:39:50