A Logic Puzzle

[tom h]

In the spirit of http://www.turbobuick.com/forums/turbo-lounge/211066-solve-riddle.html , submitted for your approval :


Determine which of the following statements in the list are true and which are false:

1. Exactly one of the statements is false.
2. Exactly two of the statements are false.
3. Exactly three of the statements are false.
4. Exactly four of the statements are false.
5 Exactly five of the statements are false.
6. Exactly six of the statements are false.
7. Exactly seven of the statementsare false.
8. Exactly eight of the statements are false.
9. Exactly nine of the statements are false.
10. Exactly ten of the statements are false.

 

[Studmonkey]

#9 true the rest are false. #9 being true means the other 9 are false. You can't sat it for any other ones

 

[tom h]

Buick guys are just too smart This took you all of 5 seconds to solve!

here's a slight variation of the same puzzle, basically I have removed the requirement "exactly" :

Determine which of the following statements in the list are true and which are false:

1. one of the statements is false.
2. two of the statements are false.
3. three of the statements are false.
4. four of the statements are false.
5 five of the statements are false.
6. six of the statements are false.
7. seven of the statements are false.
8. eight of the statements are false.
9. nine of the statements are false.
10. ten of the statements are false.

 

[Studmonkey]

#8 is true the rest are false? The same being that #1 is false and not are false I think Getting late but the Penguins won, been drinking, just got glasses for reading and my head hurts. Those are my excuses

 

[Studmonkey]

Would be more compeling if #1 was one of these statements are true then say # 3 was 3 of these statements are also true.

 

[tom h]

Nope, sorry, try again

 

[Studmonkey]

Tired 8 and 1 are true the rest false? In the first sentence is, and not, are matters or 9 and 1 are true? maybe?

 

[jpratt]

all are true.

 

[tom h]

all are true.

No; If all were true, then at least one statement would be self-contradictory, for example :

10. ten of the statements are false.

This cannot be a true statement, because it asserts that all the statements (including #10) are false

 

[Studmonkey]

9 again?

 

[tom h]

Hint for the 2nd puzzle - the wording is equivalent to

Determine which of the following statements in the list are true and which are false:

1. one or more of the statements is false.
2. two or more of the statements are false.
3. three or more of the statements are false.
.
.
.
9. nine or more of the statements are false.
10. ten or more of the statements are false.

well , strictly speaking you can't have "ten or more" (as there's exactly 10 statements), but that's not a trick or even relevant, I just did it to preserve the symmetrical appearance of the sentences.

 

[Studmonkey]

the first 9 are true

 

[Studmonkey]

Hint for the 2nd puzzle - the wording is equivalent to

Determine which of the following statements in the list are true and which are false:

1. one or more of the statements is false.
2. two or more of the statements are false.
3. three or more of the statements are false.
.
.
.
9. nine or more of the statements are false.
10. ten or more of the statements are false.

well , strictly speaking you can't have "ten or more" (as there's exactly 10 statements), but that's not a trick or even relevant, I just did it to preserve the symmetrical appearance of the sentences.

That was noe equivalent at all.

 

[tom h]

That was noe equivalent at all.

Well, consider:

1. one of the statements is false. ​

Even if you had one, two, or three false statements somewhere in the list, then #1 is true ... it is not limited to "exactly one" as the 1st puzzle was.


That's why I thought re-phrasing slightly to

1. one or more of the statements is false.
2. two or more of the statements are false.
... etc
​

could be a hint, of sorts.

 

[tom h]

The self-consistent answer to the 2nd puzzle :

1 thru 5 are true
6 thru 10 are false