The Trolley Problem
It seems to me the solution to The Trolley Problem1 is that the viewer should throw themselves under the wheels, in the hope of a derailment.
Dare I say it, the standard arguments2 don't seem to reflect well on our society3.
Notes:
1 (1967) "The Problem of Abortion and the Doctrine of the Double Effect." Oxford Review, Number 5.
2 The best summary on current thinking on the Trolley Problem is:
(2014) "A Review and Systematization of the Trolley Problem." Philosophia 42, 251–269 (ResearchGate).
3The same goes for the discussions of Kierkegaard on Abraham, and of Judges 11:30-40. I note that Foot implies almost the same thing in her original paper, noting in a similar example: "...it would be reasonable to act, though one would respect someone who held back from the appalling action either because he preferred to perish rather than do such a thing..."; she just doesn't note it as a solution.