What's the right way to hard boil eggs? I find I always have trouble scaling the amount of time the eggs should be boiled, cooled, etc. for different-sized batches of hard-boiled eggs.

I've heard a variety of "folk lore"-type rules for how it should be done, but what's really the right way?
I've never adjusted the length of time based on number of eggs. As long as the water is boiling I don't think it would take any longer to cook a dozen than to cook one (it might take the water longer to come up to boiling, I guess).

For hard boiled I normally bring them up to the boil and then turn the heat off, and leave them for 15 minutes. If you like them less well-cooked, you could reduce this to 12 minutes. Then empty the pan and re-fill it cold water a couple of times to cool them down quickly. Leave rest of them sitting in the cold water while you prepare each one.