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The Ten Statements (Posted on 2003-02-25) Difficulty: 3 of 5
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 ?

See The Solution Submitted by Ravi Raja    
Rating: 3.6250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: method of proof | Comment 35 of 61 |
(In reply to method of proof by Cory Taylor)

Hey Cory, you have stated 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", well i think these conditions are enough to remove away all the impossible cases (i mean the ones which lead to paradoxes, wrong solutions and other confusing answers) and then since the two have to be equal, all you are left with is to decide whether the statements 1 through 5 will be true or the statements 6 through 10. That's it and you'll be done. No other explanation or any other cases using trial and error is to be used after this i believe. What do you have to say about this ?

  Posted by Ravi Raja on 2003-02-28 21:01:31

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