Scott the Painter

This is an obvious guess-and-try problem, but its real value lies in teaching us not to assume too much.

From the list of heuristics, #2, guess and try, and #17, check for hidden assumptions.

This problem is easily understood, and students are willing to dig in on it. If students are working on it in class, I'm ready for somebody to blurt out the question, "Does he have to start in room 1?" That question gives the game away, which is okay with me. The point is for students to see that they need to be on the lookout for unnecessary assumptions, and whenever that point gets brought out is fine.

Once students realize that Scott does not have to start painting in room #1, they will quickly find more than one solution. Here are a couple of possibilities:

4-3-2-1-5-6-7-8-12-11-10-9-13-14-15-16

13-9-5-1-2-6-10-14-15-11-7-3-4-8-12-16

This problem goes very fast, and once students see that Scott can start in rooms other than #1, it is natural to ask which rooms Scott can begin in so he can paint them all, and which rooms won't work as starters? There is a pattern to be found and some thinking to do about why the pattern works.

Further extensions are possible: What if there aren't 16 rooms, but 9, or 25, or some other perfect square? What if the configuration of the rooms is not a square, but a rectangle?