I was reading an article on Slashdot this morning about the hiring process at Google and some readers chimed in with other experiences wherein an interviewee was required to work through a "deep-think" type question during the interview. An example was pirates, quoted below.
five pirates have 100 gold coins. they have to divide up the loot. in order of seniority (suppose pirate 5 is most senior, pirate 1 is least senior), the most senior pirate proposes a distribution of the loot. they vote and if at least 50% accept the proposal, the loot is divided as proposed. otherwise the most senior pirate is executed, and they start over again with the next senior pirate. what solution does the most senior pirate propose? assume they are very intelligent and extremely greedy (and that they would prefer not to die).
The answer to this -- and many examples of other questions of this type -- are available on the techinterview.org website.