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 Post subject: A Maths question.
PostPosted: Mon Jun 10, 2013 9:53 pm 
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You have eight switches. Each switch has three possible positions; off, neutral or on. In order to turn on a light you must use three of the eight switches, in either a 2 off 1 on combination, or a 2 on 1 off combination. The other 5 unused switches are to remain neutral. Only 1 combination will turn on the light. How large is the pool of possibly correct combinations?

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 Post subject: Re: A Maths question.
PostPosted: Mon Jun 10, 2013 10:16 pm 
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Start by calculating the possible combinations of 3 out of 8 (8C3)=56. Out of those ones, you have to eliminate the ways that you can have 3 on and 3 off. I think that it means you can have 54 ways, though I'm a bit rusty when it comes to stats...

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 Post subject: Re: A Maths question.
PostPosted: Mon Jun 10, 2013 10:17 pm 
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There are (8 choose 3)=56 ways to select which three you're going to use. Once you specify that, there are six ways to arrange the 3 switches (three choices for which switch is the odd one out, and two choices for whether or not the odd one out is on or off). Assuming I understood your question right, that's 56*6=336 possible arrangements.


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 Post subject: Re: A Maths question.
PostPosted: Mon Jun 10, 2013 10:22 pm 
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Assuming all the switches start in the neutral position:

Choose 3 of the 8 switches to be part of your solution. (8 choose 3) = 8! / (5!*3!) = 56. For the 3 chosen switches, there are 2^3 = 8 ways to change them from neutral. Two of these are not feasible [all on / all off], but the other 6 are combinations of 2 on / 1 off or 2 off / 1 on. Thus, there are 56*6 = 336 possible solutions.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 11:19 am 
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The answer is 1, because the question clearly states that only one combination works, so that is technically the only "possibly correct combination". The fact that we don't actually know what the correct combination is, is irrelevant. :P

PS. Yes, I know this is not what the question was looking for, but I always liked to go against expectations by thinking outside the box and bending the rules. My teachers used to hate me for that because I would insist that my answer was still technically correct and argue, disrupting the entire lesson! Eventually they learned to just accept my answers as correct and ask if anyone else had an "alternative answer". :lol:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 12:48 pm 
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So, Kelvin, you were a PITA like me :shock:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 3:29 pm 
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Gus wrote:
So, Kelvin, you were a PITA like me :shock:

Yes, but I think the word the teachers used in the staffroom began with a different letter. :shock: :shock: :shock:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 5:28 pm 
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Sorry Kelvin, you'd lose that debate in my class (If I had one). Only one combination is correct, yet the question asks how large the pool of possibly correct combinations is, you, not knowing which combination is correct, have a pool of 338 "possibly" correct combinations to chose from. :P

Thank you guys! I ask because I recently purchased a lock for my collection shown here:

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That is a slightly later release of the lock, resistant to both decoding methods shown here:
http://www.youtube.com/watch?v=artxM_TtWgo
and here:
http://www.youtube.com/watch?v=zMnwzXLLHUE

I quickly realized there weren't too many possible combinations as it is, so I set about trying all of them, I wanted to know how many there were.

Thank you guys!
(not you Kelvin :D )

Edit:
P.S. The lock functions as the light functions in the original question.

Edit2ForKelvin: If I place two cups in front of you, upside-down, and say one cup has a ball underneath it, there are two possibly correct choices, yet only one is actually correct. I covered my butt by saying "possibly."

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Last edited by EMarx on Tue Jun 11, 2013 5:39 pm, edited 1 time in total.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 5:35 pm 
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EMarx wrote:
Sorry Kelvin, you'd lose that debate in my class (If I had one). Only one combination is correct, yet the question asks how large the pool of possibly correct combinations are, you, not knowing which combination is correct, have a pool of 338 "possibly" correct combinations to chose from. :P

Wrong, I don't need to know which is the correct combination to know how many combinations can possibly be correct. Hence, there can only be one possible correct combination, because that is what the question tells us. 8-)

Sorry, but you *can't* win this one. :lol:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 5:44 pm 
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The question tells you there is only one actually correct combination.

I'd like to refer you to the second edit of my second post, and I would like to expound on the idea, in order to show how you are wrong. :D

Of the two cups, one has a ball. I charge you with the task of telling me which cup has the ball. You can exclaim "There are two possibly correct choices!" You cannot exclaim "There is one possibly correct choice!" As that would imply the ball may not exist at all, and I have lied to you.

Concede defeat!

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 5:48 pm 
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No, I won't concede defeat, ever...

Maybe I'm looking at the problem from the perspective of the person who set up the wiring and therefore does know the correct combination. Indeed, the question doesn't tell me what perspective I must see the problem from. Therefore, the answer is one, and I am right. :D

PS. By adding a second example problem to clarify your original question, you are simply trying to add further information and meaning, essentially admitting that your original question wasn't properly defined and so, in my mind, you have already conceded defeat. :wink:

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Last edited by KelvinS on Tue Jun 11, 2013 5:58 pm, edited 1 time in total.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 5:56 pm 
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To support that argument, you would need to change the wording of my original question from "possibly" to "possible." The difference between those words is huge.

Even knowing the combination, there is only one "possible" combination that is correct. There are 338 that are "possibly" correct. But my question clearly states "possibly," thus knowing or not knowing the combination is irrelevant.

Now report to detention!

Edit: I have added a second example in order to simplify the reasoning process. The logic applies directly and I can reconstruct the exact same arguments using the original question. In having to have this conversation, I assumed a simpler example would be just that.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:04 pm 
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In your question, "possibly" is used as an adverb to modify the verb "is" in relation to the word "correct", which has the same meaning as using the adjective "possible" directly in conjunction with the word "correct", therefore you are trying to imply a difference in meaning where there is none. Seems like you are now clutching at straws. :D

Either that, or you've used the adverb "possibly" with no verb at all, in which case your question is just bad grammar and therefore meaningless...

Concede defeat!

PS. Usually by now the lesson would have ended and the teacher would have stormed out for a cigarette! :lol:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:19 pm 
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You, sir, are grabbing at straws by modifying the rules of grammar in order to continue to suit your frail and failing argument.

I have used "possibly" as an adverb to modify the verb "correct."

My question is still airtight.

I've been a step ahead of you the entire time!

Concede!

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:21 pm 
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So with the word "correct" now intended as a verb rather than an adjective, you are now talking about "possibly correcting" the combinations. What nonsense! :lol:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:30 pm 
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Ah that is nonsense. I concede defeat on that one point!

In my haste to beat you, I have erred. But where you have erred, is in assuming that adverbs always have to modify a verb, wherein adverbs can modify adjectives. My adjective here being "correct" to describe the combination.

Now I have won for good. (Possibly?)

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:36 pm 
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Actually, you are right on that point, but it does not change the fact that the "number of possibly correct combinations" has the same meaning as the "number of possible correct combinations". Hence your argument based on the difference falls apart.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:39 pm 
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I am sorry, but you can't POSSIBLY be implying that two different parts of speech, with different intended usages and meanings are exactly the same. That isn't POSSIBLE. Do you see the subtleties in the what those usages are implying?

Eric:5
Kelvin:1

Edit: Just so the moderators don't accuse of us of getting off-track, I assure you this is debate over the answer to the original question, not a battle of egos in any manner, shape, form or resemblance thereof.

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Last edited by EMarx on Tue Jun 11, 2013 6:46 pm, edited 1 time in total.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:45 pm 
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But here you are now using the word "possibly" with a compound verb (can't be) rather than an adjective, so you are creating a difference artificially by using the words "possible" and "possibly" in two completely different contexts. Otherwise there would be no difference in meaning.

PS. Yes, this is one big joke for me, I'm enjoying this completely pointless debate and smiling to myself mostly at how silly we are both being. :lol:

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 6:57 pm 
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Agreed. The pool of possibly or possible correct combinations doesn't change. It is still 338. Whether you know or not.

In order to to support your answer of "only one answer is possible" you would then need to modify a verb, thus deviating from my original statement of "possibly" as an adverb modifying an adjective, changing the meaning and voiding your answer.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 7:08 pm 
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EMarx wrote:
Agreed. The pool of possibly or possible correct combinations doesn't change. It is still 338. Whether you know or not.

But I know it's 1 ... Because that's what your question tells us.

By the way, what was the question again? :lol:

OK, I'm getting bored, and will concede defeat this time, but only on the point of perseverence, not on the answer, which is still 1. :D

I need to sleep.

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 11, 2013 7:13 pm 
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"It's" here being a compound verb of it is, a point I addressed in the second half of my last post.

Thus I win in both perseverance and the answer being 338.

It's only 20:00 in New York here, so I'm full of vigor and debate.

Thanks Kelvin. That was fun. :D

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 Post subject: Re: A Maths question.
PostPosted: Tue Jun 18, 2013 12:34 am 
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I concede already!

Dave :)

Note: Any post with this many contributions alternating between two people indicates an opportunity for the PM feature of this forum...

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