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.
http://www.demarcken.org/carl/papers/ITA-software-travel-com...
false positive = allowing bad candidate to pass
False positive = Type II error
Personally, I find these problems interesting but the one I liked the most was the instant search because it had an element of user interaction rather than mere algorithmic problem solving, so I guess I might be the one filtered out :)
For my solution, I tried both tries and hash tables, and I found them to perform at more or less the same level. I later experimented with suffix trees, which I think is probably the best way to go for that problem.
Actually it sounds like a pretty easy problem from this far out, but maybe if I actually worked on it I'd discover it was trickier than I thought.