http://www.manhattangmat.com/forums/post9689.html
there probably isn't a "shortcut" in the way you're defining a shortcut; the solution outlined in that post is, in all likelihood, essentially the same as yours.
here's my best suggestion for saving time on this problem:
realize that the shortcut-free method will work, and START IT RIGHT AWAY. do not stare at the problem; as soon as you've thought of something, ANYTHING, that will solve it, just do it.