a head-scratcher(redirected from head scratcher)
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A thoroughly complex or difficult mystery, problem, puzzle, or riddle. I'm not sure how we'll be able to reach an agreement with the labor unions on this issue. It's a head-scratcher, to be sure. A: "What is weightless but can be seen, and if you put it in a bucket, it will make the bucket lighter?" B: "Hmm, I don't know. That's a real head-scratcher!"