1
general::
Phrase(s): (It) beats me. [and] (It’s) got me beat.; You got me beat.
Inf. I do not know the answer.; I cannot figure it out. The question has me stumped. (The stress is on me.) • Bill: When are we supposed to go over to Tom’s? Bill: Beats me. • Sally: What’s the largest river in the world? Bob: You got me beat.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
This baffles or puzzles me, as in I don't know how he does it? beats me! This term originally may have alluded to a winning poker hand. It may Also be related to the even earlier usage of beat for "astonished" or "at a loss." [Slang; mid-1800s]
American Heritage Idioms