Essential Understanding 4.2 of the AP CS Principles curriculum is as follows: "Algorithms can solve many, but not all, computational problems." Among the topics I am expected to cover in the context of this standard are algorithms that run in a reasonable time v. those that don't, the difference between solvable and unsolvable problems, the use of a heuristic, and the existence of undecidable problems.

My plan is to cover the 0/1 knapsack problem, the heuristic of a greedy algorithm, and the halting problem. This is a relatively small part of the course and is assessed by only a couple of multiple-choice questions on the AP Exam, so I don't need more than one lesson (or two) of material.

That said, I am afraid any one-day lesson will be inevitably reductive as these are complex topics. Moreover, the students are new to programming and computer science in general, so I need to balance abstract with theory with concrete, relevant examples.

What lesson ideas, examples, and/or analogies do well to serve the teaching of this standard?