a paradox is solved by finding the error in the seemingly valid logic. sometimes this requires unintuitive logic, and it more often than not requires thinking outside the box.
let me give a few examples to illustrate the point.
paradox of the heap of sand: one grain of sand is obviously not a heap. a million grains of sand is obviously enough to be a heap. one additional grain of sand does not make a non-heap into a heap. but then, when does a non-heap become a heap?
answer: the falsehood here is the implicit assumption that a collection of grains of sand is either 100% a heap or 100% not a heap with no middle ground. a “heap” is a mental schema, a mental class of things as it were, and since the human brain does not operate in absolutes, something can be “sort of a heap.” the weak point here is the law of excluded middle (a statement can only be true or false); setting it aside resolves the paradox.