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 The Ten Statements (Posted on 2003-02-25)
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 ?

 Submitted by Ravi Raja Rating: 3.6250 (8 votes) Solution: (Hide) If all 10 are false then this is exactly what the 10th asserts. But if it's true, we get a contradiction since then not all 10 are false. Hence, at least one is indeed false. On the other hand, no two of the statements may be true simultaneously; for they make contradictory assertions. Therefore, exactly one of them is true while the remaining nine are false. This is what is claimed by the ninth statement. This is true too. And for the second part, "The First Five are TRUE and the Last Five are FALSE".

 Subject Author Date A guess K Sengupta 2007-03-16 11:14:18 Software program solution Penny 2004-10-15 23:22:47 Easy Lewis 2003-06-14 00:39:50 The k statements Tim Axoy 2003-06-03 12:42:42 On and on Tim Axoy 2003-05-12 06:19:02 Hard logic Tim Axoy 2003-05-12 02:38:13 re: 1 to 5 Ravi Raja 2003-03-20 20:30:52 1 to 5 Tim Axoy 2003-03-20 06:19:47 re: Without exactly Ravi Raja 2003-03-19 23:35:27 re: Without exactly Ravi Raja 2003-03-19 23:31:36 re(2): Without exactly Ravi Raja 2003-03-19 23:22:07 re: Without exactly Ravi Raja 2003-03-19 23:14:07 re: Without exactly Charlie 2003-03-19 16:34:08 Without exactly Tim Axoy 2003-03-19 12:38:27 re: 9 is true. Ravi Raja 2003-03-13 19:55:34 re: 9 is true. Ravi Raja 2003-03-13 19:53:38 9 is true. Tim Axoy 2003-03-11 05:13:11 re: i know the answer!!! Ravi Raja 2003-03-05 04:24:37 i know the answer!!! aiai 2003-03-04 05:14:25 re: Ravi Raja 2003-03-01 21:48:14 re(3): Still Doesnt Make Sense Ravi Raja 2003-03-01 21:43:07 Hmmm thinking...(this is the same as the No Subect post) Lucifer 2003-03-01 09:26:59 No Subject Lucifer 2003-03-01 09:25:46 re(2): Still Doesnt Make Sense Lucifer 2003-03-01 09:17:42 re(2): method of proof Ravi Raja 2003-03-01 04:25:54 re: method of proof pleasance 2003-03-01 02:31:10 re: method of proof Ravi Raja 2003-02-28 21:01:31 re: Still Doesnt Make Sense Ravi Raja 2003-02-28 19:00:53 re: method of proof Ravi Raja 2003-02-28 18:51:28 re: possibly... Ravi Raja 2003-02-28 18:44:26 Still Doesnt Make Sense Lucifer 2003-02-28 12:26:19 method of proof Cory Taylor 2003-02-28 04:45:15 possibly... fad 2003-02-28 02:13:36 re(3): This doesnt make sense Ravi Raja 2003-02-27 19:40:10 re: Solution Ravi Raja 2003-02-27 19:37:12 re(3): This doesnt make sense Ravi Raja 2003-02-27 19:32:46 re: self reference Ravi Raja 2003-02-27 19:06:34 re: self reference Ravi Raja 2003-02-27 18:58:56 Solution Gautam 2003-02-27 16:18:27 re(2): This doesnt make sense Lucifer 2003-02-27 13:40:11 self reference pleasance 2003-02-27 05:37:24 re(2): solution 2??? Ravi Raja 2003-02-27 03:02:31 re: solution 2??? Ravi Raja 2003-02-27 02:59:55 re: Seems easy Sasha 2003-02-26 21:41:54 re: solution 2??? Sasha 2003-02-26 21:41:03 solution 2??? Sasha 2003-02-26 21:38:19 is it a paradox ??????/ Ravi Raja 2003-02-26 19:29:09 re(3): i think i've got it Ravi Raja 2003-02-26 19:25:29 re: This doesnt make sense Ravi Raja 2003-02-26 19:20:12 re(3): i think i've got it Ravi Raja 2003-02-26 19:14:23 re: solution?? Ravi Raja 2003-02-26 18:46:09 re: Seems easy Ravi Raja 2003-02-26 18:41:41 This doesnt make sense Lucifer 2003-02-26 17:37:02 re(2): i think i've got it Sasha 2003-02-26 11:11:24 solution?? Wayne Berry 2003-02-26 11:03:38 Seems easy Scott 2003-02-26 10:44:30 re: i think i've got it Ravi Raja 2003-02-26 04:35:07 re: i think i've got it Ravi Raja 2003-02-26 04:32:53 re: solution Ravi Raja 2003-02-26 04:29:22 i think i've got it Sasha 2003-02-25 23:16:06 solution Cory Taylor 2003-02-25 08:28:42

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