[Warik]

I might be wrong, but I don't think there's enough information here for Logician C to be able to say "my number must be 50" - assuming of course he really is a "perfect" logician.

Why?

Assume A = 20, B = 30, and C = 50.

C KNOWS FOR A FACT that A's number is 20 and B's number is 30.

C also KNOWS FOR A FACT that his number is thus either 50 (30 + 20 = 50) or 10 (20 + 10 = 30).

Another poster said that C would know that he was 50 because if B saw 20 and 10, then he'd know that he was 30 because you can't duplicate the 10. Ok... fine... but who says B didn't see 20 and 11? B could see 20 and 11 and then not know if he was 9 or 31. C doesn't know what's on his forehead, and I'm assuming the 3 individuals are not allowed to share information. C has no idea what B saw, and thus can't act on that information.

So... B knows that he sees 20 and 50... and he KNOWS that since he doesn't see one of the two perfect sets of numbers (numbers which must be either added or subtracted to arrive at the correct result because the other operation would result in duplication), he can't guess his own number... however, C does not know which number he has on his forehead, and so he can't use B's lack of ability to arrive at a conclusion to determine his own number, since as far as "C" knows, 50 and 10 are just two of the infinite possibilities "C" could have written on his forehead.

Now... I don't have an answer for a possible solution to this puzzle... just pointing out that I think the solutions presented already (which are acting on the above principle) are fallible.

I think more information is required in the problem statement to arrive at a conclusion here.

Either that or I've had too much to drink and have made an ass of myself.

Let me know either way. thx.