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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 05, 2013 5:41 am 
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Well, I thought it was assumed that the battery was already connected. I would also like to add:
Spoiler:
He'd have to conduct this experiment far away enough to notice a difference. For example, if he's too close, all the tests will have the same result. Further away, however, results will vary assuming that the wires resist electrical flow differently. How far away, who knows? I'm a doctor, not a technician, dammit!

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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 05, 2013 5:50 am 
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I'm not sure I understand. What would he have to be far away from? And it should be assumed that all wires have essentially the same, low resistance.


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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 05, 2013 3:04 pm 
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If it sounds confusing, then it probably is. Not because it's complex, but because of my ignorance on the subject. I can draw a picture if you'd like. It'll probably make no more sense, but why not? I'll wait to see if anyone else solves first. If not, then I'll draw picture.

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 Post subject: Re: Logic Puzzles
PostPosted: Mon Dec 09, 2013 3:22 pm 
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Disappointed by the lack of interest in this puzzle. Here are a couple of hints for anyone who wants to try to solve the puzzle on their own, and following is the solution, since three days have passed since I posted the puzzle:

Hint 1 - the circuit
Spoiler:
If the technician connects two wires together at one end, he can test to see whether they're connected at the other end by using the light bulb and the battery right next to each other. For those who know a little less about electricity, a light bulb has two terminals. One must be connected to the + of the battery, and the other to the -. The battery can be connected to the terminals either directly or via a wire. Therefore, the light bulb would light up if the following circuit was completed:
Battery (+ or -) -> Wire (Joined at the technician's end)
Wire -> Wire (Joined together previously by the technician at the other end)
Wire -> Light Bulb (Joined at the technician's end)
Light Bulb -> Battery (whichever terminal was not used before)


Hint 2 - the minimum walking distance
Spoiler:
The minimum walking distance is 4km. Since the cable is 2km long, this means that he he starts at one end, walks to the other end (2km) where he can label every single wire, then walks back to the first end, and is able to label them on that end too.


Hint 3 - a little more electronics
Spoiler:
The technician could connect the wires together in bundles so that the circuit could be completed in a number of ways. For example, if 10 wires were connected at one end, at the other end, if the battery and light bulb were connected to one of those 10, nine others would complete the circuit.


Hint 4 - relating to how it's possible
Spoiler:
The number 120 is relevant. Something about it makes this method possible. Wikipedia tells me that 120 is the factorial of 5, a triangular number, a hexagonal number, tetrahedral number and a perfect number (among other things). One of these qualities makes this particularly efficient method possible.


Hint 5 - revealing the quality (Hint 4)
Spoiler:
This method is only possible with triangle numbers. Perhaps try to do it with a smaller triangle number.


Solution:
Spoiler:
The technician starts by connecting the wires at one end into bundles of 1, 2, 3 ... 13, 14, 15 wires, and labels them according to which group they belong to. He then walks to the other end. At this end, he is able to determine which group each wire belongs to by testing to see how many other wires complete the circuit. (He would not be able to complete the circuit for the group of 1, and 14 other wires would complete the circuit for the group of 15.) Once he has done this, he arranges the wires into new groups using the following method: He takes one wire from each of the 15 groups to make up a bunch of 15, then takes one wire from the remaining 14 groups (there's only 14 groups left since one "group" only contained one wire) to make up a bunch of 14. He continues this method until he has 15 new groups. He then adds an additional label so that each wire has two labels, which correspond to the group that it was in the first time, and the group that it is in now. No wire will have the same two labels. The technician then walks back to the other end of the cable. He can use the same method as before to identify the new groups, and once he has done this, he can add the second labels. The labels are unique, and will match up at both ends of the cable. Done.


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 Post subject: Re: Logic Puzzles
PostPosted: Wed Dec 11, 2013 4:00 pm 
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With this thread moving so slowly, I'm not quite sure why I chose to adhere to the Three Day rule and post the solution to my last puzzle. Clearly we've all run out of ideas and so it would've been in everyone's interest to allow it to exist for a while longer. Perhaps a hint every three days would've been more appropriate. Oh well, what's done is done. However, I have a new puzzle for you all:

A movie theatre seats 100 people. The first person in line has a valid ticket, but a printing error makes it impossible to determine his seat. The usher advises him to sit wherever he wants. The rest of the patrons have legible tickets and will either sit in their designated seat or, if their seat was taken, wherever they like. This particular screening is sold out. What is the chance that the last person to enter sits in the seat on their ticket? (And more importantly, why?)


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 Post subject: Re: Logic Puzzles
PostPosted: Wed Dec 11, 2013 11:49 pm 
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Spoiler:
1/93326215443944152681699238856266700490715968264381621468592963895217
59999322991560894146397615651828625369792082722375825118521091686400
0000000000000000000000. I looked up 100! on google and got his number. Not sure if right or wrong, though.


I think. Maybe.... :S

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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 12:09 am 
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Incorrect. Sorry.


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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 4:20 am 
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Spoiler:
1/100. Because the other 99 seats are taken, whatever seat he gets has a 1/100 chance of being his seat. He can't know for sure due to the printing error. Now I see why 100! is wrong. Because no one knows whose seat is whose.

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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 5:08 am 
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That is also incorrect.

If anyone is struggling with this, feel free to ask for yes/no questions or hints. It will be much more interesting than not participating.


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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 7:39 am 
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Spoiler:
Say we have N spectators. For N=2, the probability would be Р(2)=1/2. For greater N values, using the primitive recursive function, we would get the following formula: Р(N) = 1/N * (1 + Р(N-1) + Р(N-2) + ... + Р(2)). Making use of the modern scientific progress achievements, we get a revelation that Р(100)=1/2 (as it would be for any N>1).

Basically, if a person enters last and only one seat remains unoccupied, this person has only two variants: either it is his/her seat, or someone else's, the person's seat already being occupied. Which makes for a 50% possibility.

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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 9:09 am 
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Correct! Well done, Norroen. And nice explanation also. Where were you for my last puzzle? It could've used a few more heads working on it. Oh well. Your turn, if you have something.


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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 12:22 pm 
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Does that mean I have a 50% chance of being hit by a flying tiger on my way to the store, seeing as I either will be or wont be?

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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 1:13 pm 
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Yes, Taters. Yes, it does... In case you didn't get Norroen's explanation (I can't tell), I'll explain it in another way:
Spoiler:
In this case, there are just two seats that matter: The first person's seat, and the last person's seat. Every time someone finds that their own seat has been taken, which could happen up to 100 times, if they happen to choose one of these two seats, the outcome is known. Every other seat is irrelevant - it just means that the outcome will be determined later on, when one of those seats is taken. If the first person's seat is chosen, then everyone from that point on will get their own seat (including the last person). If the last person's seat is chosen, then obviously they won't be sitting in it. So essentially it's about which one gets chosen first, and there is absolutely no reason to think that a patron is more likely to choose one or the other - it's entirely random and therefore 50%.


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 Post subject: Re: Logic Puzzles
PostPosted: Thu Dec 12, 2013 1:50 pm 
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New quickie:

Spoiler:
Don Pedro was walking along minding his own business, when he was accosted a bunch of desperados.
Spotting the large gold signet ring on Don Pedro's finger, they attempted to pry it off, but it would not come loose - so they cut off the entire finger. Throughout the entire gruesome scene, Don Pedro did not let out a single sound. Question: why didn't Don Pedro call for help, knowing the he is not mute?

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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 3:10 am 
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Spoiler:
If he had screamed, the criminals would have probably killed him. But because of his compliance, the criminals spare him.


But for some reason, I think I might be wrong yet again. Seems too easy. There's got to be a catch. Unless the catch was no catch. :shock: ...probably not.

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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 4:08 am 
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Nope.

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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 4:25 am 
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Spoiler:
I am going to guess that the was giving them the ring willingly for some reason or other. Perhaps they needed the ring for a reason that would be beneficial/necessary for him?


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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 4:27 am 
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The finger was a prosthetic?

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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 12:36 pm 
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Is Don Pedro a chimp or monkey perhaps?


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 Post subject: Re: Logic Puzzles
PostPosted: Fri Dec 13, 2013 1:47 pm 
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No correct answers so far. :S
This is one of the riddle types where, in theory, any solution may be accepted, whether logical or humorous. But since it's not a riddle of my invention and it has an 'official' answer, let's keep guessing. :wink:

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Dec 14, 2013 12:01 am 
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Spoiler:
Because he doesn't care about his finger being cut off.


Obviously. :roll:

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 Post subject: Re: Logic Puzzles
PostPosted: Sat Dec 14, 2013 12:14 am 
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Spoiler:
Did he steal the ring?


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Dec 14, 2013 4:41 am 
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Unfortunately, no correct answers so far. :S

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But why bounce around to the same damn song?
You'd rather run when you can't crawl...


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Dec 14, 2013 11:02 am 
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He and the desparados were in the vacuum of space, so he knew no one would hear him scream anyway.


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 Post subject: Re: Logic Puzzles
PostPosted: Sat Dec 14, 2013 11:19 am 
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Don Pedro had already been killed/knocked into unconsciousness by the desperados? :P

A desperado sat on Don Pedro's face? :wat:

Okay, for an actual attempt... Don Pedro did not scream because the ring was already tight around his finger, which constricted the blood and stuff and left the finger numb and without feeling? :S


I don't know, there must be a thousand possible answers for this that could work.

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