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Math Help - a combinatorics problem

  1. #1
    cos
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    a combinatorics problem

    I have B different labels and C different objects. Each label can be assigned to more than one object at the same time, and each object can have more than one label.

    I want to assign every label to exactly X of my C objects, while ensuring that no object has more than Y different labels.

    For some values of C, this will not be possible. My question is: What is the smallest value of C for which I can do this assignment?
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  2. #2
    cos
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    my solution

    ...is in the next post....
    Last edited by cos; July 23rd 2010 at 03:42 AM.
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  3. #3
    cos
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    my solution

    I think the lowest number of objects is given by

    X if  B \leq Y
    and  X+(B-Y)\left\lceil X/Y \right\rceil otherwise

    where with B \leq Y we have every object getting all labels, and so X objects are required, while otherwise  \left\lceil X/Y \right\rceil extra objects are required to be assigned the labels not used up by the first X objects.
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