I should probably have qualified that bit, yes. *g* see if the mapping is non-surjective then there are people who do not have an assigned prompt and can attempt any of the others, non-injective means assigning several prompts to the same person - not ideal. OTOH, looking at the map - now no longer an inverse - going the other way, non-injective means assigning several people to the same prompt, whereas non-surjective means some prompts do not have any people assigned - bad! Of course, since our sets are not infinite the First Isomorphism Theorem shows that if we want the first map to be injective and the second map to be surjective both of these imply |{P : P is a prompt that must be completed}| < |{W : W a writer}|, so by the Pigeonhole Principle not every writer can generate a prompt. :)?

One of the very good things that has come out of this post on my part is learning about the NYR challenge! A bit unfortunate now, but definitely something I will be looking at after New Year's!