Which number of cousin you are tells you how far back in generations the relation is. First cousins share a set of grandparents, second cousins share great-grandparents, and so on.
Number removed tells you the difference in generation from the other person. So if your first cousin has a child, that child is your first cousin, once removed. The relationship you share with them is your grandparents, but their great-grandparents. One generation different, so we say once removed. That child’s child would then be your first cousin, twice removed, and so on.
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