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Thread: Student and reward

  1. #1
    Senior Member Vinod's Avatar
    Sep 2011

    Student and reward

    A room has 100 boxes labelled 1 to 100.The names of 100 students have been placed in these boxes by principal.The students shall visit the room one by one.Each student is allowed to inspect the contents of at most 50 boxes, one after the another and leave the room with no communications with other students.If the student discovers his own name in the boxes he inspects,he will get a reward.The students are allowed to collude beforehand and devise a strategy to maximise the chances of getting a reward to each and every student.What is their strategy?
    I am trying to answer this question but right now, I don't have any answer.If anyone knows the answer,let me know it.
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  2. #2
    MHF Contributor
    Nov 2010

    Re: Student and reward

    It depends on the rules. Are the boxes allowed to be moved? What about their contents? I'd say, the first student collects the names from the first 50 boxes and puts them all in box #1. The second student collects the names from boxes 51 through 99 and adds them to box #1. First student has a 50% chance of a prize. Second student has 99% chance of prize. Every student after has 100% chance for a prize.

    Another possibility: leave open specific boxes vs closing them. This would be another solution. The students order themselves in alphabetical order by last name. The first student to enter will leave open the box of every student whose last name is among the first 50 students and keep closed the remaining boxes. The second student will check boxes 51 through 100, similarly leaving open every box containing a name whose last name is at the beginning of the alphabet. But, this could be considered communication.

    Alternately, if you deem "communication" to be any difference between when the student arrived in the room to the time they leave as "communication". If no method of communication is allowed, of any kind at all, then every student has a 50/50 chance of finding his/her name, regardless of any strategy chosen.
    Last edited by SlipEternal; Apr 11th 2018 at 11:07 AM.
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