The Kloster solution[0] solves it in a more direct way, by showing that for each action the devil takes the angel can take a counter action by limiting it's own moves.
In the one proof is the realization that sometimes it's easier to solve a smaller problem then prove equivalence to a harder problem, and in the other is the realization that sometimes voluntarily reducing the number of actions can lead to a simpler solution. Both are pretty good tools to have under one's belt.
Seems like Kloster devised a mathematical proof for a kiting - a game strategy that involves staying just out of the effective range of an opponent while they chase you.
In the one proof is the realization that sometimes it's easier to solve a smaller problem then prove equivalence to a harder problem, and in the other is the realization that sometimes voluntarily reducing the number of actions can lead to a simpler solution. Both are pretty good tools to have under one's belt.
[0] - http://home.broadpark.no/~oddvark/angel/kloster.html