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A rectangular puzzle fits perfectly inside of a frame. The magician adds a new piece and rebuilds the puzzle, yet somehow they still form a rectangle that is exactly the same size, a Perpetual Puzzle. The puzzle still fits perfectly in the frame. When you add another piece and rebuild the puzzle again, the puzzle impossibly still forms the same exact size rectangle, and fits perfectly within the same frame.
This magical puzzle is a masterpiece of ingenuity. The more you add, the more things remain the same. While your audience may surmise that the rearrangement of pieces enables this baffling puzzle to work, they will never suspect that the frame and cardboard also contain subtle gimmicks. It is this disarming combination that allows you to perform a truly impossible illusion.