Sentence:  Both these youths , who greatly admired Henrietta , were somewhat younger than she , as were also the neighboring Friedenwald boys , who were then studying medicine ; and bright though they all were , they could not <WSD>possibly</WSD> compete for her interest with Papa , whose mind - although he never tried to dazzle or patronize lesser lights with it - naturally eclipsed theirs and made them seem to her even younger than they were . 
Meaning of the word marked with <WSD> tags:  by chance