If something totally stumps you, doesn't make one lick of sense and has no logical explanation, then it's safe to say it mystifies you.
To mystify is a verb that sounds not so mysteriously like mystery. That's because something that mystifies is just that. There's no answer or explanation to be found for it. If you're mystified, you're in awe and bewilderment. The infinite nature of the universe mystifies some people. Others are mystified by the appeal of teen sensations from Ricky Nelson to Justin Bieber.