I'd put my hand over its mouth as tight as possible for as long as needed, hoping it would survive by breathing through its nose..
If it came down to killing it or not, I'd have to kill it. As you decided in my question, the needs of the many outweigh the needs of the few.. Which is funny because I have a book that has a few situations where this doesn't apply (utilitarianism), I'll see if I can dig one of those scenarios up for you..
I have one of those scenarios.
The example you listed with the fat man and train(s) is a thought experiment originally proposed by Phillipa Foot, an ethical philosopher. Awesome thought experiment, I did my thesis on it. TEEHEE!
We discussed the idea of creating a 'new' threat, or simply diverting an already existing threat and the differences between them.
Let's say it's war time, and a nuclear missile is headed for New York. In this example, New York has a population of 5,000,000 people and is an area designeated as 'high risk', because it's such an essential city. Essentially, the government was suspecting an attack on New York, and has made it clear to citizens of New York that the threat level is high.
There are only two courses of action, one is to let the missile hit New York, the original target, where people were
warned that an attack could be incoming OR launch your own missile (this is the only option) to divert the missile attack towards Newark, a smaller city, with fewer people appox 1,000,000, but a city that the citizens were NOT warned of incoming attacks and no attacks were expected.
Basically, the citizens of New York decided to stay in New york regardless of the warnings of an incoming attack, is it OK to divert the missile to a city where people were assumed to be safe just to mitigate losses?
Does the fact that the people of New York were warned and chose to stay mean they should sleep in the bed they made? Or should the utilitarian ethical argument still ring true?
What about if for whatever reason, the only course of action to save New York was to bomb Newark yourself, for example let's say the only way to stop the bomb was to detonate a bomb in it's path, which happened to be exactly where Newark is located.
So now, it's not even the enemies bomb, it's YOUR bomb that would be required to kill the 1,000,000 people of Newark not the enemies..... hmmmm.... what do you do?