I would like to know if this question 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 (a box may contain different types of objects). We are allowed to look inside the boxes, then have to select a set of boxes that contains at least half the number of each type of object. What is the least number of boxes for any given k and n to guarantee that this is possible, regardless of the distribution of the objects?