Often problem sets are of the form "Given X, now show Y". So you know your end point.
Sometimes you know the route pretty intuitively, sometimes it's not intuitive at all and you just do a bunch of manipulations of X until you think you see the route.
Sometimes you don't see the route and it just looks more and more complicated and you're wondering if you're really up to doing this sort of thing.
And then you glance at it, and you see how to reorganize to let 90% of the monstrosity drop out, leaving you Y.
It's a good feeling. Knowing the route intuitively is a good feeling, but it's very encouraging to trudge through a mess of greek letters and operators - not knowing your route at all and just hoping you haven't messed something up - and then realizing at the end that you actually stayed accurate the whole way through.
Report from Brownbackistan!
55 minutes ago