In my opinion the most awesome and funny exercise I recieved so far was in art. We listened a short lecture about the Möbius strip (a thingy which has no distinction between upside and downside face and only one edge but forming a ringlike object will transform your brain into some similar structure if you really try to understand it). The task was to take the Möbius strip and to think it one step farther and get some not yet known use, object or generel piece of art.
The Möbius strip beeing a two dimensional object that can only excist in three dimension as it twist in a way that is impossible in only two dimensions has a three dimensional counterpart the Klein bottle, which is basically a volume that is twisted in the fourth dimension to recieve an object that has no distinguishable in- or outside. To be able to understand that horrible wiggly thing you need to project it into three dimensional space where it can only be displayed with a selfintersection (in the fourth dimension it won't intersect).
Me and a fellow student did a quick brainstorm (I will write something about that subject soon as it is a very productive method of gathering and improving ideas) and produced a whole lot of ideas ranging from Möbius texts that end where they start, but twisted over Möbius videos wher the camera follows a Möbius strip to a Möbius projection of a closed ring-street section. We decided to go for a fourth option and went to lunch.