Sideshow Bob to Lisa Simpson - "Oh I see. When I try to kill you, it's nothing to get worked up about, but as soon as my brother does, it's 'hopeless - utterly hopeless !'"
The sense that something is impossible is often an emotional reaction to a frustrating situation. Those of us who like puzzles appreciate challenging problems, and we're often able to find solutions to seemingly hopeless predicaments.
To someone who enjoys problems, being beset with problems is like being beset with candy.
When faced with that which is frustrating and the truly impossible, consider what psychologist Marsha Linehan said. Acceptance is not liking something. It's learning to live with something.