The trolley problem is an ethical thought experiment. In it, a trolley is moving fast down a track towards a switch. There are two tracks beyond this, on which one and five people respectively are tied up. If the trolley is not stopped, it will run over five people, killing them; the switch can divert it onto the second track, with just one person on it.
The trolley problem is easily solved by Newtonian spatially corrected total utilitarianism, the correct ethical system, as explained in Implications Of a Newtonian Model for Spatially-Varying Ethical Reasoning and Considerations on Multi-Event Moral Significance Scaling.