Puzzle/maths problem

[glenatron]

Emperor Alexius of Barzantium has six most trusted advisors in his cabinet: Bericus, Constantine, Davidius, Esquilinus, Fabius and Gesius. One of them however is a traitor, spying for the rival empress Zoe of Foobia. Alexius knows that any of his own agents that empress Zoe is aware of will be executed, but as a question of security he likes to keep the identities of his agents secret from everyone. He knows he will have to give away some of them in order to identify the spy. What is the smallest number of agents he can betray to definitely identify the spy?

This isn't a standard puzzle question really (or at least, it is, but I'm not setting it as a puzzle ) it's more a fundamental maths/computer science question that I feel should be intuitively obvious to me and is probably about the underlying principles behind bitmasking or parity that I've never really explored far enough to master. So assuming this is a standard question does anyone know what it is called? If it is not a standard question does anyone have any interesting answers to it? I feel there should be a solution that gives away no more than three spies, but I haven't yet found my way to it.

Comments

[glenatron.livejournal.com]

This overlapping sets approach is the one I'm thinking of.

I now realise that it depends on whether you know the outcome of each round of information before starting the next one as well.

If each round we know the answer to the previous one you can quickly eliminate people. If you have to plan ahead a complete scheme it's obviously much more complex. Intuitively I feel it should be doable in n attempts where the number of untrustworthy advisers <= 2^n.

[thewhitespider.livejournal.com]

Yeah, that's a difference between this test and parity checking.

You might need to start thinking about eight or sixteen bits of data, to see how it scales.