I mean, the 'perfect logicians' part put me into thinking like '...and if there are 3 BlE and 100 BrE, and the Guru says 'I see at least 1 BlE', then at that moment each one of the three BlE thinks there's 2/3 chances she means either of the other two, so next time just before noon, when they converge again, one of the three BlE finds the other two and goes away without saying anything. Then if next morning the two others are found to have left, he knows he's chance of being the only BlE left has gone up and presents himself for inspection. When he is confirmed as BlE, next time it automatically releases all BrE. Now let's consider the case of four BlE present...' etc. I doubt it can be done easily for large groups of people, though, unless they cooperate. The easiest way to do it is to appear before the Guru in pairs:)