My colleague Gayle Smith at LCC passed along a link to a nice collection of "non-routine mathematics problems" named Stella's Stunners, created by the Ohio Resource Center.
Scott the Painter
Scott the painter is going to paint the floors of 16 rooms. He is in room #1. He can go through any door (see diagram). He cannot return to any room once he has painted it--slow-drying paint! In what order should he paint the rooms? Obviously, #16 must be last.