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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.
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  5. #325
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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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    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.

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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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    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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    Re: Monty Hall, we have a PROBLEM

    Supposedly, one of the hardest su doku puzzles ever devised can be found here: http://nypost.com/2010/08/22/its-the...-su-doku-ever/


    I have not really looked at it too closely, at least not yet.
    "Hope is a good thing; maybe the best of things."

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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by FreshFish View Post
    Ecclesiastes 1:9
    All of Ecclesiastes 1 is beautiful:

    The words of the Preacher, the son of David, king in Jerusalem.
    Vanity of vanities, saith the Preacher, vanity of vanities; all is vanity.
    What profit hath a man of all his labour which he taketh under the sun?
    One generation passeth away, and another generation cometh: but the earth abideth for ever.
    The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose.
    The wind goeth toward the south, and turneth about unto the north; it whirleth about continually, and the wind returneth again according to his circuits.
    All the rivers run into the sea; yet the sea is not full; unto the place from whence the rivers come, thither they return again.
    All things are full of labour; man cannot utter it: the eye is not satisfied with seeing, nor the ear filled with hearing.
    The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun.
    Is there any thing whereof it may be said, See, this is new? it hath been already of old time, which was before us.
    There is no remembrance of former things; neither shall there be any remembrance of things that are to come with those that shall come after.
    I the Preacher was king over Israel in Jerusalem.
    And I gave my heart to seek and search out by wisdom concerning all things that are done under heaven: this sore travail hath God given to the sons of man to be exercised therewith.
    I have seen all the works that are done under the sun; and, behold, all is vanity and vexation of spirit.
    That which is crooked cannot be made straight: and that which is wanting cannot be numbered.
    I communed with mine own heart, saying, Lo, I am come to great estate, and have gotten more wisdom than all they that have been before me in Jerusalem: yea, my heart had great experience of wisdom and knowledge.
    And I gave my heart to know wisdom, and to know madness and folly: I perceived that this also is vexation of spirit.
    For in much wisdom is much grief: and he that increaseth knowledge increaseth sorrow.
    Last edited by Kepler; 04-12-2017 at 12:35 PM.
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    Re: Monty Hall, we have a PROBLEM

    Okay, Ralph has 184,013 posts, and he is averaging 28.36 posts per day. At that rate, when will he reach 200,000 posts?
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  14. #334
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by ShirtlessBob View Post
    Okay, Ralph has 184,013 posts, and he is averaging 28.36 posts per day. At that rate, when will he reach 200,000 posts?
    When he decides to post again after making post #199,999.
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by ShirtlessBob View Post
    Okay, Ralph has 184,013 posts, and he is averaging 28.36 posts per day. At that rate, when will he reach 200,000 posts?
    Sometime between November 21, 2018 and November 22, 2018. Maybe the 200,000th post will be the great reveal of who killed JFK on the 55th anniversary of his death.
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  16. #336
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by Fighting Sioux 23 View Post
    Sometime between November 21, 2018 and November 22, 2018. Maybe the 200,000th post will be the great reveal of who killed JFK on the 55th anniversary of his death.
    Wasn't JFK killed on 11/23? Nothing good comes from the #23.
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by St. Clown View Post
    Wasn't JFK killed on 11/23? Nothing good comes from the #23.
    November 22, 1963. Oswald killed November 24th. 23 is really the only good number left.
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by St. Clown View Post
    Nothing good comes from the #23.
    Not a Michael Jordan fan, eh?
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  19. #339
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by FreshFish View Post
    Not a Michael Jordan fan, eh?
    He was pretty good in Creed, but Fantastic Four had some serious issues. I don't think they were his fault, nor do either of those movies contain the #23.
    "The party told you to reject the evidence of your eyes and ears. It was their final, most essential command." George Orwell, 1984

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  20. #340
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    Re: Monty Hall, we have a PROBLEM

    Quote Originally Posted by Fighting Sioux 23 View Post
    November 22, 1963. Oswald killed November 24th. 23 is really the only good number left.
    I was in a HS English class. I remember the rumor of his death spreading and the teacher denying it could have happened, but probably inwardly happy based upon his political bent.
    Last edited by Ralph Baer; 05-10-2017 at 01:55 PM.

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