Be sure that all students understand the statement and agree on the wording. Have the students look at the map of Puzzzletown and solve the Ice Cream Stands Puzzle for this map. Tell the students that, just as with Twotown, there will come a point when they are trying to reduce the number of Ice Cream Stands that they use, where they will see it is impossible to use any fewer Ice Cream Stands. Have the class again collaborate to compose a clear explanation of why the solution they have found for Puzzletown is the minimum. The chain of reasoning to do this is more complicated than what was required for Twotown.
Some students are likely to grasp the reason before others do.
Invite the students to try other dominating set puzzles to see if they can always be so sure their solution is the best one. Most people find the Puzzletown problem harder than the Twotown one. To verify the Puzzletown solution, you have to hold a lot of information in your head all at once. Talk about how difficult it is to explain something to someone who hasn't understood it in the same way as you do, and how difficult it is to try to understand something that someone else is explaining to you. Make a list of ideas that would be good advice for everyone who is either struggling to explain or struggling to understand.