As a native English speaker and qualified teacher of English I would say that my answer 'I will just win' is better than 'I will barely win' which sounds translated. I was marked wrong.
"I will just win" also means "I will win by a small margin". Same kind of usage as in "I will just fit through that door", or "I will just have enough cash for dinner" or "I will just make it across the road in time to avoid the oncoming semi-trailer".
Hrrrmmm, 'I will only just win' is maybe better?
It's a silly sentence anyway, I wonder if there's any Germans on here that can tell us whether anyone would ever actually say this in German, it seems like a really odd sentiment to me.
That is what I tried as well. Really looks like it should be accepted so I reported it.
'Barely' means 'kaum', not 'knapp'. 'Knapp' in this context means 'close' (as in, 'it was very close, but I won')