I would like to now if this [question][1] on Stack Exchange can be generalised. We generalise the problem as follows. There are k types of object and n boxes each which may contain any number of objects. If we know the contents of each box, what is the minimum number of boxes we must select to guarantee getting at least half of each type of object.

  [1]: http://math.stackexchange.com/questions/2542/100-boxes-with-apples-oranges-and-bananas