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Mind challange when friends buys a car

  1. Nov 6, 2011 #1
    Four friends A, B, C and D are buying a car together.
    They agree that everyone should have one of the first four trips all alone.

    But the following conditions apply:

    1. If D is allowed to get on the first trip, C would have the third trip.

    2. If A or D take the second trip, C would have the first trip.

    3. If and only if A receives the third trip, B want to have the second trip.

    4. Will D get the third trip, A wants the second trip.

    5. Will D get the last trip would C have the third and A the first.

    In what possible orders can they take the first four trips so that all is happy?
    Motivate your answer.

    Good luck,folks!! =)
     
  2. jcsd
  3. Nov 6, 2011 #2

    I like Serena

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    Welcome to PF, Grinder! :smile:

    CABD, CDAB, or CDBA
     
  4. Nov 6, 2011 #3
    :smile: Thanks!!

    You have to justify the thought. Are there more? ;)

    /Grinder
     
  5. Nov 6, 2011 #4

    Dale

    Staff: Mentor

    Unless I am misunderstanding the conditions, your first answer violates condition 5, and your second answer violates condition 3. Only your third answer satisfies all 5 conditions. Additionally there is
    CADB

    Justification is an exhaustive search of all possibilities :smile:
     
  6. Nov 6, 2011 #5

    I like Serena

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    Oops! I mistyped my first solution and miss checked my second solution. :redface:


    No, there are no more:

    It is easiest to verify the possibilities for D.
    If D is first, the rules dictate uniquely when the others go, leading to a contradiction.
    With D second, the order has to be CDBA.
    With D third, CADB follows.
    Finally with D 4th, we get another contradiction.
     
  7. Nov 6, 2011 #6
    Hi!

    What about ACDB and BCDA then? :wink:

    What conditions are they violate? Or do they satisfy all conditions?? :smile:

    /Grinder:biggrin:


    and yes....I found the smilie button!!:surprised
     
  8. Nov 6, 2011 #7

    I like Serena

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    "4. Will D get the third trip, A wants the second trip."
     
  9. Jan 6, 2012 #8
    every one is wrong here... i will tell you how...
     
  10. Jan 6, 2012 #9
    go back read the question again and solve it...
     
  11. Jan 6, 2012 #10
    ACDB and BCDA is wrong
     
  12. Jan 6, 2012 #11
    It is easiest to verify the possibilities for D. but If D is first, the rules dictate uniquely when the others go, leading to a wrong answer.With D the order D has to be CDBA.With D third, CADB follows.Finally with D fourth, we get another wrong answer.
     
  13. May 6, 2012 #12
    Hi everyone,

    Unless I am misreading the question, the answer is ABCD. To me the list of conditions is just that a list. IF this one does this than that one will be satisfied if he does this. In that case the only condition that has everyone happy in the end is condition 5 If D is last then C wants to be third and A wants to be first. That leaves B to be second.

    Did I misread the question?
     
  14. Jul 27, 2012 #13
    Unless I am mis-reading this, the answer is CADB
     
  15. Aug 4, 2012 #14
    This one wasn't too hard. I came up with the following answer, if there's any flaws I'd like them to be pointed out.
    CDBA
     
  16. Sep 6, 2012 #15
    CADB @@v hehe.. If I understood it correctly?
     
  17. Nov 27, 2012 #16
    I don't think that I understand this correctly
     
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