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#1
05-26-2005, 08:10 AM
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Logic Problem
Posted this in OOT a few days ago without any interest (did get 1 possible (I think incorrect) answer, but no explanation from DBowling).
Anyways, here's the problem: Below are ten statements concerning X, a whole number between 1 and 10 (inclusive). Each statement may or may not be true. What number is X? 1. X equals the sum of the statement numbers of the false statements in this list. 2. X is less than the number of false statements in this list, and statement 10 is true. 3. There are exactly three true statements in this list, or statement 1 is false, but not both. 4. The previous three statements are all false, or statement 9 is true, or both. 5. Either X is odd, or statement 7 is true, but not both. 6. Exactly two of the odd-numbered statements are false. 7. X is the number of a true statement. 8. The even-numbered statements are either all true or all false. 9. X equals three times the statement number of the first true statement in this list, or statement 4 is false, or both. 10. X is even, or statement 6 is true, or both. 
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#2
05-26-2005, 08:25 AM
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Re: Logic Problem
I have a solution to the problem... but will let everyone else have a shot at it.
The original wording was "Not all of the statements are true, but not all of them are false either." When I looked at the statements it did not take me long to prove that they logically could not all be true and logically could not all be false, either. That threw me off for a while, because for some reason I thought that was a key piece of information and that it was somehow a trick question. That's why I reworded it here...
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#3
05-26-2005, 08:58 AM
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Re: Logic Problem
[ QUOTE ]
Each statement may or may not be true [/ QUOTE ] intuitivly i think you have to say each statement is either true or false i'm guessing this whole thing revolves around statements like: this statement is false are these kind of statements allowed? your original wording seems to imply these statements are allowed, where as my wording i reckon says these statements are not allowed ....what i am saying may or may not be true [img]/images/graemlins/tongue.gif[/img]
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#4
05-26-2005, 09:16 AM
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Re: Logic Problem
Yes, that's why the original wording threw me off so much.
I thought that the fact that NOT all the statements are true, and NOT all the statements are false, would eliminate 9 of the 10 possible numbers (i.e. they would all have to be true or all have to be false for all incorrect answers). However - a better way to look at the problem is not to guess the actual number, but to try to evaluate each statement. You'll see alot of contradictions arise; if this is true then this has to be false; if A and B are true, then C has to be false, but then D has to be true, and E has to be false, but that makes A false - thus this combination of T/F's does not make sense. Just giving some examples... from my analysis if you look at it carefully enough, only one combination of true/false assignments makes sense logically - and the number is derived from those statements.
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#6
05-26-2005, 09:32 AM
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Re: Logic Problem
[ QUOTE ]
[ QUOTE ] thus this combination of T/F's does not make sense [/ QUOTE ] ah ok, i'm on the same wave length now, so each statement has to be either strictly true or strictly false yeah? [/ QUOTE ] Yeah, something like that. You're not allowed to have something be true and false at the same time, if that's what you're saying... Certain combinations don't work logically. For example, statement 1 and 2 both can't be true. Statement 8 clearly indicates that at least one of statements 2, 4, 6, or 10 are true (if they are all false, then if 8 is false, 8 would be true, but then 8 would be false, but then 8 would be true.... etc.)
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#10
05-26-2005, 11:22 AM
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Re: Logic Problem
Several of the statements contradict. The two most obvious (at least to me) were statements 9 and 4. They either both must be true or both false. Assume one or the other and see where it takes you. I assumed true. From there work through each statement logically until something fits. Once you evaluate one and two as being false and three as true, statement nine gives the value of X. From there, work through each statement and make sure nothing eliminates the number 9 as a possible answer.
That's how I did it. It actually takes a bit of trial and error. For example, if you assume statement one is true, then X=3 according to statement nine. But this will be eliminated as a possible answer when you work through the rest of the statements.
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