There have been some reasonable challenges in the comments below to my claim that the ticking time bomb scenario is impossible. So let me add this:
The impossibility lies, not in the idea that a catastrophic evil will occur, but in the idea that you have perfect knowledge about the villain before you.
As it is actually proposed in discussion, yes, it is often proposed in terms that are literally impossible. I've seen this most in attempts to move away from scenarios that can and do actually occur. If, say, someone points out that interrogated prisoners are often ignorant of any plots, or even completely innocent, another person might reply, "Yeah, but suppose in this one case we just absolutely know that this guy's involved in a plot."
Such literally impossible scenarios can be cleaned up, by adding things like "morally certain," so that they are no longer literally impossible. That does not necessarily make them possible. It remains to be established that a mechanism exists for obtaining moral certainty in such circumstances. If you can't show that such a mechanism exists, then you might as well say, "Suppose you had X-Ray vision."
Note that each correction and adjustment to the ticking time bomb scenario moves us away from the dramatically imagined and toward the real world. Which brings me to one of my other major points: Why don't we start with the real world, and worry about the imaginary world only after we've figured out the real world?
That last is not entirely a rhetorical question. Why is the ticking time bomb question so universally irresistible?
The best answer I can think of is one I mentioned in my last post: Hypothetical scenarios can be very helpful in understanding different facts of an issue.
I ask, then: How helpful has the ticking time bomb scenario been in understanding different facets of this issue?