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

[life-of-tom.livejournal.com]

Yeah, I'm having a hard time understanding the question. Do you mean that no-one's ID is publicly known, if they are publicly known then she'll kill anyone who isn't her man?

In which case, I can't see myself how 'betraying' one person gives you any more information than 'that person is or is not the spy,' and the corresponding information about the others.

[glenatron.livejournal.com]

Alexius does not know who the traitor is, but he does know who his spies are. His advistors, including the traitor, do not know who his spies are. If the traitor hears about a spy they will inform the Empress Zoe and the spy will be executed.

For some reason Alexius is more interested in preserving the secrecy of his spies identities than he is in their survival, so he is willing to sacrifice several spies to identify the traitor rather than identify six spies and have a simple one-to-one correspondence and have the identities of five spies known by people other than himself. He is very much of the opinion that information is power. But not information gained from living spies, apparently