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Title: True or False, Quick and dirty. Post by Noke Lieu on Apr 16th, 2012, 9:51pm Statements are either true or false. Which is which? (It's pretty hard to proofread your own ones of these, so I quantum-apologise in advance) 1. Statement 2 is false. 2. Statement 1 is false. 3. Statement 2 is true. 4. Statement 6 is true. 5. Statement 3 is false. 6. Statement 5 is false. 7. Statements 1 and 2 can’t both be false. 8. Exactly 6 statements are true. 9. Exactly 4 statements are true. 10. Statement 8 is true |
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Title: Re: True or False, Quick and dirty. Post by towr on Apr 16th, 2012, 10:22pm [hide]Either 1,5 and 7 are true, xor 2,3,4,6 and 7 are true; 9 is true xor 8 and 10 are true. Combining one of the former two groups with one of the latter two groups gives 1,5,7,9 being true as the only possibility.[/hide] |
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Title: Re: True or False, Quick and dirty. Post by Noke Lieu on Apr 16th, 2012, 11:39pm *phew* I'm not firing on all cylinders at the moment, and I couldn't swear that I got it right. That said, I don't think it's quite right for the intended use. But I'll get around that. |
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Title: Re: True or False, Quick and dirty. Post by SMQ on Apr 17th, 2012, 4:42am on 04/16/12 at 22:22:25, towr wrote:
No. [hide]8, 9, and 10 all false is also consistent.[/hide] Unfortunately for Noke Lieu, that means there are [hide]three completely consistent solutions: T,F,F,T,F,F,T,F,T,F (as towr found), but also T,F,F,T,F,F,T,F,F,F (with 3 true statements) and F,T,T,F,T,T,T,F,F,F (with 5).[/hide] --SMQ |
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Title: Re: True or False, Quick and dirty. Post by Noke Lieu on Apr 17th, 2012, 5:39am :'( ...ah well, I'll get onto fixing it. I don't think the first part (1-6) needs to be so long, because the interesting part is the last 3... |
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Title: Re: True or False, Quick and dirty. Post by Grimbal on Apr 17th, 2012, 8:09am on 04/17/12 at 04:42:46, SMQ wrote:
I see, that is when #4 is placed "logically" after #6. |
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Title: Re: True or False, Quick and dirty. Post by SMQ on Apr 17th, 2012, 6:36pm on 04/17/12 at 08:09:28, Grimbal wrote:
eh? --SMQ |
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Title: Re: True or False, Quick and dirty. Post by Noke Lieu on Apr 18th, 2012, 12:17am Here we go. (I think?) 1. Statement 2 is false 2. Statement 1 is false. 3. Statements 1 and 2 can’t both be false. 4. Statements 2 and 3 are both true. 5. There are exactly 3 true statements. 6. Statement 5 is true. It's a lot easier, you can eyeball it, but checkign that it's the only solution still produces that squiffy feeling... |
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Title: Re: True or False, Quick and dirty. Post by SMQ on Apr 18th, 2012, 5:13am Looks good to me: [hide] 3 is true. 4 implies 2 implies not 1, and the contrapositive, so for the first four, either F,T,T,T or T,F,T,F. 5 and 6 are either both true or both false. Given F,T,T,T, 5&6 true implies 5 false, but 5&6 false implies 5 true: contradictions. Given T,F,T,F, 5&6 true implies 5 false, but 5&6 false is consistent. Therefore T,F,T,F,F,F is the only consistent solution. [/hide] --SMQ |
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Title: Re: True or False, Quick and dirty. Post by Grimbal on Apr 18th, 2012, 9:49am on 04/17/12 at 18:36:52, SMQ wrote:
One of your solutions starts with "T,F,F,T,F,F". I would read from that that #4 is true and #6 is false. But #4. says that #6 is true, so it cannot be. But I agree with your solutions if I read the truth of the sentences in the order 123564789X. This order is a bit more logical in the sense that then, the 7 first questions refer to earlier statements. |
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