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Thread: Monty Hall, we have a PROBLEM

  1. #321
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    Re: Monty Hall, we have a PROBLEM

    OK, so the answer to this poser is fairly straightforward, I liked it because it was an interesting twist on an old stand-by.

    There is a set of triplets that is identical in appearance in every way, so that they are hard to tell apart. One thing that does distinguish them is that, among Jack, Jim, and Joe, Jack and Jim always answer a question with a lie, and Joe always answers a question truthfully.

    You see one of them approaching you. You need to find out if it is Jack or not, since Jack owes you money. You can only ask him one question. What question do you ask that lets you know which one he is?




    PS I do know that identical triplets are extremely rare; this is a logic problem using idealized assumptions....
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    Quote Originally Posted by FreshFish View Post
    OK, so the answer to this poser is fairly straightforward, I liked it because it was an interesting twist on an old stand-by.

    There is a set of triplets that is identical in appearance in every way, so that they are hard to tell apart. One thing that does distinguish them is that, among Jack, Jim, and Joe, Jack and Jim always answer a question with a lie, and Joe always answers a question truthfully.

    You see one of them approaching you. You need to find out if it is Jack or not, since Jack owes you money. You can only ask him one question. What question do you ask that lets you know which one he is?




    PS I do know that identical triplets are extremely rare; this is a logic problem using idealized assumptions....
    Answer below:

    "Is Jim your brother"

    Jack will answer no, Joe and Jim will answer yes.

  3. #323
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    Re: Monty Hall, we have a PROBLEM

    Okay. I am aiming for 1,000 miles running on the year. I average 35 miles a week, and am currently at 269 miles run so far for the year. What I want to know is this:

    1. When will I reach my goal for the year?

    2. At this rate, how many miles could I run in total for the year?

    This is assuming that all remains well, no injuries, illness, etc.
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by ShirtlessBob View Post
    Okay. I am aiming for 1,000 miles running on the year. I average 35 miles a week, and am currently at 269 miles run so far for the year. What I want to know is this:

    1. When will I reach my goal for the year?

    2. At this rate, how many miles could I run in total for the year?

    This is assuming that all remains well, no injuries, illness, etc.
    Assuming that, going forward, week starting 2/26/2017, you have 269 miles already, then at 35 additional miles per week, you should hit 1,000 miles during the week starting 7/16/2017 (1,004 miles at the end of that week).

    Continuing that 35 miles / week pace all year brings you to 1,809 miles by the end of Saturday, 12/30/2017.
    "Hope is a good thing; maybe the best of things."

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  5. #325
    Defacing this tagline is a MAX foul Twitch Boy's Avatar
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    Re: Monty Hall, we have a PROBLEM

    I saw this one right away, but really had to grapple with where the "error" was.

    Three guys (or gals) walk into a hotel and ask for a room.

    The manager tells them the bill will be $30. The three guests decide to split the bill evenly - each pays $10. They go up to their rooms.

    A couple hours later the manager realizes he screwed up, the bill should only have been $25. He calls over his bellhop, hands him $5, and tells him to take the money up to the three guests.

    The bellhop realizes there's no way to divide $5 evenly among three people, and the guests are none the wiser, so he decides to give them each $1 and keep the remaining $2 for himself as a tip. He goes up and gives each guest $1 and puts $2 in his pocket.

    Each of the three guests has now paid $9 for the room, for a total of $27. The bellhop has $2. That accounts for $29. Where is the missing dollar?

    There isn't one. The guests have paid $27. The manager is up $25 and the bellhop is up $2. We're all square.

    The "error" is at the very end of the problem. When I mention the bellhop's $2 tip, I'm really counting it twice. (For the accounting geeks, I'm adding debits and credits.) The $27 (formerly $30) the guests are out already accounts for it.

    Alternatively, you can think of the tip as being in the $5 the manager gave to the bellhop - that's $25 for the manager, $3 for the guests, and $2 for the bellhop, all $30 is accounted for.

    Imagine if the room had only cost $10, and the manager gave $20 back to the bellhop to take to the guests. He gives them each $1 and keeps $17 for himself. Guests have paid $27, bellhop kept $17, that's $44 which has nothing to do with anything. The $29 is a red herring.
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by Twitch Boy View Post
    I saw this one right away, but really had to grapple with where the "error" was.

    Three guys (or gals) walk into a hotel and ask for a room.

    The manager tells them the bill will be $30. The three guests decide to split the bill evenly - each pays $10. They go up to their rooms.

    A couple hours later the manager realizes he screwed up, the bill should only have been $25. He calls over his bellhop, hands him $5, and tells him to take the money up to the three guests.

    The bellhop realizes there's no way to divide $5 evenly among three people, and the guests are none the wiser, so he decides to give them each $1 and keep the remaining $2 for himself as a tip. He goes up and gives each guest $1 and puts $2 in his pocket.

    Each of the three guests has now paid $9 for the room, for a total of $27. The bellhop has $2. That accounts for $29. Where is the missing dollar?

    There isn't one. The guests have paid $27. The manager is up $25 and the bellhop is up $2. We're all square.

    The "error" is at the very end of the problem. When I mention the bellhop's $2 tip, I'm really counting it twice. (For the accounting geeks, I'm adding debits and credits.) The $27 (formerly $30) the guests are out already accounts for it.

    Alternatively, you can think of the tip as being in the $5 the manager gave to the bellhop - that's $25 for the manager, $3 for the guests, and $2 for the bellhop, all $30 is accounted for.

    Imagine if the room had only cost $10, and the manager gave $20 back to the bellhop to take to the guests. He gives them each $1 and keeps $17 for himself. Guests have paid $27, bellhop kept $17, that's $44 which has nothing to do with anything. The $29 is a red herring.
    I had the same experience. It's funny because I went through 3 phases:

    1. Hey, yeah, where did the extra dollar go? (2 minutes)
    2. Oh, I see the problem, but how would I explain it? (5 minutes)
    3. Certainty of the explanation after which I can't see how I was even confused in the first place.

    That was a fun little examination of how the brain works. Very nice!
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  7. #327
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    Re: Monty Hall, we have a PROBLEM

    it's not missing.

    they each paid in $9 to the hotel (27)
    hotel register has 25 in the drawer (30-5)

    the "change" 2 is in the bellhops pocket (paid 27 - hotel has 25)
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  8. #328
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    Quote Originally Posted by Kepler View Post
    I had the same experience. It's funny because I went through 3 phases:

    1. Hey, yeah, where did the extra dollar go? (2 minutes)
    2. Oh, I see the problem, but how would I explain it? (5 minutes)
    3. Certainty of the explanation after which I can't see how I was even confused in the first place.

    That was a fun little examination of how the brain works. Very nice!
    This one's been floating around for a long time. I might've run across it back in college, which is far longer ago than I'd care to admit.

  9. #329

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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by unofan View Post
    This one's been floating around for a long time. I might've run across it back in college, which is far longer ago than I'd care to admit.
    I heard the eponymous Monty Hall problem back in grad school in the 80s, and I'm sure it's far older than that.

    There is nothing new under the sun.
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  10. #330
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by Kepler View Post
    There is nothing new under the sun.
    Ecclesiastes 1:9
    "Hope is a good thing; maybe the best of things."

    "While I thought it was the light at the end of the tunnel, in reality it was the headlight of an oncoming train."

    "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

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