A logic puzzle

24

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  • concealer404
    concealer404 Posts: 7,440
    edited May 2010
    Kenneth Swauger wrote: »
    That's a head scratcher, Russ. Let's see what I've come up with:
    1). Let's number the switches 1,2 and 3 and the lights as A,B and C.
    2). On a piece of paper I put 1, 2 and 3 at the tops of three columns. I placed an A, B and C underneath each column. Indicating that each switch could be connected to each of the lights.
    3). If we throw switch 1 and look in the door and find light B lit we can cross off A and C from the 1 column. We can cross off B from column 2 and 3.
    4). This is where I run out of logic steam. It seems to me that switch 2 could be connected to either light A or C. And the same can be said for switch 3, either A or C.
    You only get one switch throw and one room look, so only one event can be known. I don't know.
    Ken

    Hint: Temperature. ;)
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  • [Deleted User]
    [Deleted User] Posts: 7,658
    edited May 2010
    Ah, so we need to learn something else to eliminate A or C from either 2 or 3.
    Before we throw switch 1 we throw switch 2 and leave it on for a few moments. Then return switch 2 to off and throw switch 1. Go in the room and learn two things. Which light is warm and which light is lit! Eureka!
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  • Kex
    Kex Posts: 5,164
    edited May 2010
    I had no idea that C.P. was so high brow ... I don't think I'm qualified to be a member any more!
    Alea jacta est!
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  • RuSsMaN
    RuSsMaN Posts: 17,987
    edited May 2010
    Don't feel bad, I didn't get it the first time either, and that was at an interview with Microsoft!

    Cheers,
    Russ
    Check your lips at the door woman. Shake your hips like battleships. Yeah, all the white girls trip when I sing at Sunday service.
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  • [Deleted User]
    [Deleted User] Posts: 7,658
    edited May 2010
    Hey Russ, you should have asked them if the lights were fluorescent or incandescent? It would make a difference.
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  • maximillian
    maximillian Posts: 2,144
    edited May 2010
    I'll probably be criticised for this ;) but here is a good video explaining it. Some people have already posted the answer: you should always switch your answer to increase your probability of winning.

    <object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/mhlc7peGlGg&hl=en_US&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/mhlc7peGlGg&hl=en_US&fs=1&&quot; type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object>
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  • Tony M
    Tony M Posts: 11,141
    edited May 2010
    That video made perfect sense. I can see where the odds increase if your given two chances to win. AND you happened to pick the losing door on the first try.
    Most people just listen to music and watch movies. I EXPERIENCE them.
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  • wz2p7j
    wz2p7j Posts: 840
    edited May 2010
    Ok - I flip this coin. It's a fair coin and it's not a trick question. What are the odds it will be heads or tails?

    Chris
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  • tcrossma
    tcrossma Posts: 1,301
    edited May 2010
    wz2p7j wrote: »
    ok - i flip this coin. It's a fair coin and it's not a trick question. What are the odds it will be heads or tails?

    Chris

    100%
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  • wz2p7j
    wz2p7j Posts: 840
    edited May 2010
    tcrossma wrote: »
    100%

    OK got me there :D:D:D

    What are the odds it will be heads? What are the odds it will be tails?

    Chris
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  • seeclear
    seeclear Posts: 1,242
    edited May 2010
    Original problem--I still don't buy that switching is always the right choice, I'm sticking with it doesn't matter. Because we know that the host is always going to eliminate from contention a non-winning door, it is like there is really a 50-50 chance right from the get-go, even though there are 3 doors to choose from. Once the host eliminates a losing door, there are two doors and one prize---the odds you already have the prize is 50% and the odds you will win if you switch is 50%.
    "Don't forget to change your politician. They are like diapers they need to be changed regularly, and for the same reason."
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  • bobman1235
    bobman1235 Posts: 10,822
    edited May 2010
    seeclear wrote: »
    Original problem--I still don't buy that switching is always the right choice, I'm sticking with it doesn't matter. Because we know that the host is always going to eliminate from contention a non-winning door, it is like there is really a 50-50 chance right from the get-go, even though there are 3 doors to choose from. Once the host eliminates a losing door, there are two doors and one prize---the odds you already have the prize is 50% and the odds you will win if you switch is 50%.

    It's a very famous statistics problem that has been talked about and even used in many statistics classes. Trust me, they know what they're talking about.
    If you will it, dude, it is no dream.
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  • Disc Jockey
    Disc Jockey Posts: 1,013
    edited May 2010
    I remember when this came up in Mairlyn Vos Savant's column 20 years ago. Here is her comments: http://www.marilynvossavant.com/articles/gameshow.html for some reason that link doesn't always work so here's another: http://www.marilynvossavant.com/articles/gameshow_print.html?t=64 The funniest thing I found is the math teacher who gathered the data but still refused to believe it. And the other comment that said "Maybe women look at math problems differently than men"
    "The secret of happiness is freedom. The secret of freedom is courage." Thucydides
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  • FiveORacing
    FiveORacing Posts: 105
    edited May 2010
    He wouldn't offer you a chance to change if you were wrong.
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  • DeusExa
    DeusExa Posts: 491
    edited May 2010
    Surprising so few of you have heard of the infamous Monty Hall problem.
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  • cnoat
    cnoat Posts: 315
    edited May 2010
    +1 with jastas.Building code dictates witch switch turns on the light
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  • seeclear
    seeclear Posts: 1,242
    edited May 2010
    Disc Jockey wrote: »
    I remember when this came up in Mairlyn Vos Savant's column 20 years ago. Here is her comments: http://www.marilynvossavant.com/articles/gameshow.html for some reason that link doesn't always work so here's another: http://www.marilynvossavant.com/articles/gameshow_print.html?t=64 The funniest thing I found is the math teacher who gathered the data but still refused to believe it. And the other comment that said "Maybe women look at math problems differently than men"

    My head hurts.:eek:
    "Don't forget to change your politician. They are like diapers they need to be changed regularly, and for the same reason."
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  • Tony M
    Tony M Posts: 11,141
    edited May 2010
    FiveORacing wrote: »
    He wouldn't offer you a chance to change if you were wrong.

    I was thinking the same thing...Would the show risk it for intertainment purposes?
    Most people just listen to music and watch movies. I EXPERIENCE them.
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  • RuSsMaN
    RuSsMaN Posts: 17,987
    edited May 2010
    Anyone up for a cable debate?
    Check your lips at the door woman. Shake your hips like battleships. Yeah, all the white girls trip when I sing at Sunday service.
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  • disneyjoe7
    disneyjoe7 Posts: 11,435
    edited May 2010
    I think being a Mod you could start one, and close one in 1 day. ;)

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  • concealer404
    concealer404 Posts: 7,440
    edited May 2010
    The point is, that in this scenario, is that if you pick a "goat" on your first pick, and NOT a car, and you switch after the other box is shown, you have won the car.

    You have a 66.67% chance of picking a goat. You therefor have a 66.67% chance of winning the car. Rather than the 33.33% that you started out with. I'm not sure i see why this is hard....

    Switching increases your chances to 66.67%. It doesn't start the whole scenario all over with only 2 boxes, giving you the 50% chance.
    I don't read the newsssspaperssss because dey aaaallllllllll...... have ugly print.

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  • FiveORacing
    FiveORacing Posts: 105
    edited May 2010
    I don't think it makes a difference what you picked initially. One is always empty to be shown. Now you have two boxes and one pick and it doesn't matter what you're sitting on as he's allowing you to change. It was only a one in 3 change if you can't change. Now it's 50/50.
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  • concealer404
    concealer404 Posts: 7,440
    edited May 2010
    FiveORacing wrote: »
    I don't think it makes a difference what you picked initially. One is always empty to be shown. Now you have two boxes and one pick and it doesn't matter what you're sitting on as he's allowing you to change. It was only a one in 3 change if you can't change. Now it's 50/50.

    How does it not make a difference what you picked initially? I don't understand that, to be real honest.

    The ONLY way you don't win the car in this scenario and you DID switch, is if you picked the car on your very first guess. There's only a 33.33% chance of you picking the car on your first guess.

    I don't understand where 50% comes into play anywhere.
    I don't read the newsssspaperssss because dey aaaallllllllll...... have ugly print.

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  • FiveORacing
    FiveORacing Posts: 105
    edited May 2010
    concealer404 wrote: »
    How does it not make a difference what you picked initially? I don't understand that, to be real honest.

    The ONLY way you don't win the car in this scenario and you DID switch, is if you picked the car on your very first guess. There's only a 33.33% chance of you picking the car on your first guess.

    I don't understand where 50% comes into play anywhere.



    Because you are given the choice of choosing again. After the one losing pick is revealed and you start over it's as if you never had 3. Walk into the game with only two choices, one winner one loser, that's 50/50.
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  • bobman1235
    bobman1235 Posts: 10,822
    edited May 2010
    FiveORacing wrote: »
    Because you are given the choice of choosing again. After the one losing pick is revealed and you start over it's as if you never had 3. Walk into the game with only two choices, one winner one loser, that's 50/50.

    From a statistical standpoint you are not starting over; the previous set of assumptions affects the outcome.

    Try this. Look at it this way. Same thing - you're shown three boxes, one has money, two don't. You are allowed to pick one. You pick. Then you're given the choice of keeping your pick, or choosing BOTH THE ONES you didn't pick. So you can stick with yo8ur ONE box, or you can switch and take TWO boxes. Only one of the boxes actually has money in it, but how can you argue that you are not doubling your odds by choosing two boxes?

    The only thing that's different in the question as stated earlier is you're SHOWN one of the two boxes, but it's the one that's KNOWN to be empty. You already know at lesat one of the ones is empty going in, how does its being shown to you change anything at all?
    If you will it, dude, it is no dream.
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  • tcrossma
    tcrossma Posts: 1,301
    edited May 2010
    FiveORacing wrote: »
    Because you are given the choice of choosing again. After the one losing pick is revealed and you start over it's as if you never had 3. Walk into the game with only two choices, one winner one loser, that's 50/50.

    Yeah, but increase the sample size. Let's say you have 1 million items to choose from, and you have to pick 1. That's a 1 in a million chance of you being correct. Then 999,998 of the remaining items are taken away and you are left with two items -- yours and one other.

    Do you still think it's just 50/50 odds?
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  • FiveORacing
    FiveORacing Posts: 105
    edited May 2010
    tcrossma wrote: »
    Yeah, but increase the sample size. Let's say you have 1 million items to choose from, and you have to pick 1. That's a 1 in a million chance of you being correct. Then 999,998 of the remaining items are taken away and you are left with two items -- yours and one other.

    Do you still think it's just 50/50 odds?

    So now that you have two choices, and you started with one in a milllion odds, are you going to switch?


    Let's say there were a million contestants, each one got a box. When it gets down to two players are the odds in both of thier favor to switch??


    If you flip a coin 10 times and it comes up heads ten times in a row, what are the odds it will be tails the next time?
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  • tcrossma
    tcrossma Posts: 1,301
    edited May 2010
    FiveORacing wrote: »
    So now that you have two choices, and you started with one in a milllion odds, are you going to switch?

    Of course I'm going to switch. Someone with knowledge of where the winning item is has removed 999,998 losing boxes for me.

    The chance that I initially picked the winner was 1 in a million. That means it's almost a guarantee that the winning item was in one of the remaining 999,999 boxes. If somebody will remove all but one of those boxes and let me swap, you're damn right I'll swap.
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  • tommyboy
    tommyboy Posts: 1,414
    edited May 2010
    FiveORacing wrote: »
    Because you are given the choice of choosing again. After the one losing pick is revealed and you start over it's as if you never had 3. Walk into the game with only two choices, one winner one loser, that's 50/50.

    NO no no no no.

    Yes, after the one is revealed it is 50/50. But your box YOU CHOSE BEFORE has a better chance of being the losing box. And if you picked a losing box and switch( remember, two losing boxes 66%, one winning 33%), then you WILL win no matter what. I don't know how many more ways this can be explained to you.
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  • FiveORacing
    FiveORacing Posts: 105
    edited May 2010
    tommyboy wrote: »
    NO no no no no.

    Yes, after the one is revealed it is 50/50. But your box YOU CHOSE BEFORE has a better chance of being the losing box. And if you picked a losing box and switch( remember, two losing boxes 66%, one winning 33%), then you WILL win no matter what. I don't know how many more ways this can be explained to you.



    I see it Tommy. I was assumming the eliminations were random. I missed that point. Read the question, read the question......
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