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        riddles >> easy >> Logical List
        
(Message started by: ThudanBlunder on Sep 24^th, 2008, 2:55pm)

Title: Logical List
Post by ThudanBlunder on Sep 24^th, 2008, 2:55pm

1) The number of the first true statement here added to the number of the second false statement gives the number of a statement which is true.

2) There are more true statements than false statements.

3) The number of the second true statement added to the number of the first false statement gives the number of a statement which is true.

4) There are no two consecutive true statements.

5) There are at most three false statements.

6) If this puzzle consisted of statements 1-5 only then the answer to the following question would be unchanged.

Which statements are true?

Title: Re: Logical List
Post by Sir Col on Sep 25^th, 2008, 12:44am

Mind boggling good, but I've ~~possibly~~ (edit) made a boo-boo...
[hide]
6 cannot be true as it implies that removing it does not change the number of true statements.

If 1 is true then true1+false2 = 4 (there cannot be 5 or 6 true statements as there would be no 2nd false). But as false2 = 6 the number of true statements would exceed 6.
As 1 is a false complex sentence we can infer nothing of value from it.

If 2 is true (and 1 and 6 are false) then there must be four true statements: 2, 3, 4, and 5. But 3 and 4 cannot be true as 4 contadicts it, so our supposition was wrong and 2 must be false. This implies that there are not more true than false statements, which means there are 0, 1, 2, or 3 true statements.

If 3 is true then true2+false1 >= 5, which cannot be true. So 3 must be false.

If 4 is true (and 1-3 and 6 are false) then 5 cannot be true, which means that only statement 4 is true.

If 5 is true (and 1-4 and 6 are false) then we encounter a contadiction.

Hence we conclude that there is one true statement: 4.
[/hide]

Title: Re: Logical List
Post by Grimbal on Sep 25^th, 2008, 2:59am

on 09/25/08 at 00:44:44, Sir Col wrote:

If 1 is true then true1+false2 = 4 (there cannot be 5 or 6 true statements as there would be no 2nd false). But as false2 = 6 the number of true statements would exceed 6.

I am not sure we interpret sentence 1 in the same way. It seems that to you," true1+false2" gives the number of true statements. To me, it gives the ordinal number of a sentence that is true. If 1 is true and 2, 3 are false, then 1+3=4 and 4 must be true.

Title: Re: Logical List
Post by SMQ on Sep 25^th, 2008, 5:01am

I agree with Grimbal, finding [hide]TFFTFF[/hide] to be the only solution in which all statements have well-determined truth values. If the answers to 1 through 5 are [hide]FFFTF[/hide] then statement 6 reduces to "this statement is false".

--SMQ

Title: Re: Logical List
Post by Sir Col on Sep 25^th, 2008, 5:20am

on 09/25/08 at 02:59:23, Grimbal wrote:

I am not sure we interpret sentence 1 in the same way.

Duh! :-[

Your guess was right too. I had (mis)read it as "the number of statements" as opposed to what it actually says, "the number of a statement".

Title: Re: Logical List
Post by Noke Lieu on Sep 25^th, 2008, 10:22pm

on 09/25/08 at 00:44:44, Sir Col wrote:

Mind boggling good,

I have to agree with that. ;D
I am unsure of whether I should pity TnB for coming up with it though... (whether you found it, or whether making it was easier than solving it...?)

Title: Re: Logical List
Post by vallenato on Oct 24^th, 2008, 12:44pm

if you take:
5 statements in this order:V-F-V-F-V
:)7 statements:V-F-V-F-V-F-V :)