I was recently reading about the Trolley Problem
A trolley is running out of control down a track. In its path are five people who have been tied to the track by a mad philosopher. Fortunately, you could flip a switch, which will lead the trolley down a different track to safety. Unfortunately, there is a single person tied to that track. Should you flip the switch or do nothing?
I could imagine one could come up with all sorts of similar cases (e.g. shooting down a hijacked plane is one variation I could think of).
My question is: what would Judaism say in such cases?
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