How to ace the final

You can't. Sorry.

Proof by induction on Xavier's tears: In the base case, we have Xavier shedding a single tear. For the induction step, if $H$ is a subgraph of a $w$-nearly elementary $h$-wall rooted at $S$, then we can use the induction hypothesis to conclude that Xavier will shed an infinite amount of tears. $\blacksquare$