I saw the following item in a Martin Gardner Scientific American column about 20 years ago. In the context in which he had written it, it was not a puzzle per se, but an expression of paradox -- something indeed that could NOT be solved. For some reason -- probably because of my contrarian nature -- I immediately saw that it WAS soluble and wrote to Martin Gardner who liked my solution and said he might put it in his column (although I don't know that he ever did). Here's the "impossible" puzzle....and solution.

There are two locked boxes. Each contains the other's one and only key. The only way to open the boxes is with the keys. Yet, I am able to open both boxes. How is this possible?

Solution: I am inside a large box along with the smaller box and a key to that box. I open the smaller box and inside is the key to the larger box which I now open from the inside.

People tend to jump to a particular formulation of the problem-two boxes sitting side by side, and the "solver" is assumed to be outside the problem frame. In this case, the story also has a deeper metaphorical meaning; viz., that, in order to solve what appears to be an "objective" "out-there" problem, we first need to perceive that we ourselves are part of the problem/solution space.