When you contrive, you make a plan or a plot. It may take you longer to contrive your way out of doing your homework than would to actually do it.
Even though contrive often has a false or cunning feel to it, it is not always a bad thing. Mental effort is always required though, as contrive is often used in connection with inventing schemes and plans to make something happen. Contraption, a complicated mysterious device that does something, is related to contrive. Have you ever seen a Rube Goldberg contraption? When you contrive to do something, your plan may end up being that complicated.