Everyone has fought a road map back into its cover. Here is the same puzzle, small and calm. Each crease is a mountain or a valley. First check every crossing, then try to fold the whole map down to one square, one full line at a time. Some maps pass every crossing and still won't go.
The checker searches every order of whole-line folds, so its answers are exact. Whether a fast rule decides flat folding for every size of map, with folds of any kind, has been an open question since Arkin, Bender, Demaine and colleagues posed it in 2004 — a pleasant thing to know while you are stuck.
Children can try the same maps in FlatForge on Spark & Anvil (ages 15–18).