What's the word that describes this ability/quality?

Consider imaginative (“tending to be fanciful or inventive”), resourceful (“Capable or clever; able to put available resources to efficient or ingenious use; using materials at hand wisely or efficiently” (emphasis added)), plucky (“Having or showing pluck, courage or spirit in trying circumstances”), and creative (“Tending to create things, or having the ability to create; Original, expressive and imaginative”).

In addition to jwpat7's one-word solutions, there's the phrase "able to think outside the box", which combines imaginative and creative. Distant relatives in this context are intelligent and quick witted.

I would think of flexible or adaptable as well.

All good responses so far! I'd also add the more fanciful "fleet-footed" and related, "(mental) agility"