ITA's business is all about dealing with fiendishly clever transforms on small-ish sets of data, and the results are needed Right Now. Most of the hiring puzzles revolve around that theme.

Much like any other company giving these kinds of problems, it's not about bringing out that cleverness every day, but it's about figuring out who has the ability to think in that way, along with the persistence to work on the problem until it's done.