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Topic: True or False, Quick and dirty. (Read 1501 times) |
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Noke Lieu
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True or False, Quick and dirty.
« on: Apr 16th, 2012, 9:51pm » |
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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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a shade of wit and the art of farce.
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towr
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Re: True or False, Quick and dirty.
« Reply #1 on: Apr 16th, 2012, 10:22pm » |
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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.
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Wikipedia, Google, Mathworld, Integer sequence DB
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Noke Lieu
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Re: True or False, Quick and dirty.
« Reply #2 on: Apr 16th, 2012, 11:39pm » |
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*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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SMQ
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Re: True or False, Quick and dirty.
« Reply #3 on: Apr 17th, 2012, 4:42am » |
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on Apr 16th, 2012, 10:22pm, towr wrote:| 9 is true xor 8 and 10 are true. |
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No. 8, 9, and 10 all false is also consistent. Unfortunately for Noke Lieu, that means there are 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).
--SMQ
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| « Last Edit: Apr 17th, 2012, 4:44am by SMQ » |
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--SMQ
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Noke Lieu
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Re: True or False, Quick and dirty.
« Reply #4 on: Apr 17th, 2012, 5:39am » |
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...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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Grimbal
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Re: True or False, Quick and dirty.
« Reply #5 on: Apr 17th, 2012, 8:09am » |
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on Apr 17th, 2012, 4:42am, SMQ wrote:
No. 8, 9, and 10 all false is also consistent. Unfortunately for Noke Lieu, that means there are 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).
--SMQ |
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I see, that is when #4 is placed "logically" after #6.
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SMQ
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Re: True or False, Quick and dirty.
« Reply #6 on: Apr 17th, 2012, 6:36pm » |
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on Apr 17th, 2012, 8:09am, Grimbal wrote:| I see, that is when #4 is placed "logically" after #6. |
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eh?
--SMQ
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Noke Lieu
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Re: True or False, Quick and dirty.
« Reply #7 on: Apr 18th, 2012, 12:17am » |
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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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SMQ
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Re: True or False, Quick and dirty.
« Reply #8 on: Apr 18th, 2012, 5:13am » |
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Looks good to me:
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.
--SMQ
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--SMQ
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Grimbal
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Re: True or False, Quick and dirty.
« Reply #9 on: Apr 18th, 2012, 9:49am » |
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on Apr 17th, 2012, 6:36pm, 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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