Rhombus Pile
Daniel Scher wrote a nice piece with a sketchpad interactive (http://www.sineofthetimes.org/a-geometry-challenge-from-japan/) about this geometry problem about a stack of rhombi.
The original problem: if the points on the bottom are set up so AB=12, BC=13, CD=14, DE = 15 and EF=16, what is the area of the square at the top. I love problems that don't feel like they have enough information, and this is one of those!
Like Daniel, I often investigate by building it in dynamic geometry. As I did, I found a lot to notice. Here it is in case you want to play.