From Wiktionary, the free dictionary
A shortening of it beats me
beats me
( idiomatic , as response or with indirect question) don't know ; I have no idea .
Do you have any idea what "tergiversate" means? Beats me !
Beats me how he finds out when we're goofing off.
1918 Edgar Rice Burroughs , “The Land That Time Forgot ”, in The Blue Book Magazine →OCLC Hugo Gernsback , editor, Amazing Stories (please specify |part=I to III) , New York, N.Y.: Experimenter Publishing , 1927 , →OCLC "Flowering shrubs don't thrive in the subterranean caverns from which geysers spring," suggested Bradley. Olson shook his head. "It beats me," he said.
This expression is nearly always used in the present tense, first person singular, as given above. 
