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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: 3.7778 (9 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".

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2024-05-18 00:59:34
Solution	Math Man	2023-04-27 15:43:44
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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