Back when I was a student, 25+ years ago, many professors were a bit lazy. They just re-used problem sets which they had made earlier. No single year would be alike, but the problem sets would still be from a larger collection.

The students would then hand down the big book of problem and solution sets down to the freshman class.

The professors, still being a bit lazy, knew this. But instead of scarping the old problems, they'd just say that cheating only hurts the students doing it - as the homework grades would not influence the final grade. And sure enough, the students that never did their own work, rarely did well (if at all passed) on the finals exam.