Talk:2005 USAMO Problems/Problem 5

It says that $f(i)$ is increasing by at most $1$ for each change in $i$, but I don't think that's the case ($b_i$ can increase by more than $2$). The claim that $f(i)$ has to be $0$ at some point is correct, but only because of discrete continuity. Would someone confirm this? I don't trust myself to make edits to this solution.