The search for a solution space gave an empty set when it came to crew members and that was that. While HAL undoubtedly had some life-preserving behaviors in his goals, he would -- in such a critical mission -- have had programmed in an escape hatch if presented with a kind of trolley problem wherein a crew member might live (but the mission fails) or selecting to kill a crew member (by action or inaction) and allowing the mission to go forward.
Then, by induction, he continues to subtract one from the N crew members until he would have a solution that satisfies the constraints: zero, the trivial case.
Each step of this comes down to humans.