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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?

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?

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 (the boxes don't have to only contain the same type). 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?

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?

I would like to now 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 (the boxes don't have to only contain the same type). 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.

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 (the boxes don't have to only contain the same type). 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?