So, can we get an answer here?

Oh right, sure

. The answer is:

A=2

B=3

C=5

Explanation:

A sees 3 and 5 so can only deduce that his number is either 8 (5+3) or 2 (5-3)

B sees 2 and 5 so can only deduce that his number is either 7 (5+2) or 3 (5-2), and he can't learn anything new from the fact that A does not know his number since A would not be able to figure out his number regardless of what B's number was.

C knows that he is either 1 or 5. If C was 1 then he knows that A would be able to work out that he was 2 or 4 and B would be able to work out that he was 1 or 3. B would know that he couldn't be 1 however since this would mean A would see two 1's and be able to deduce tht he was 2 immediately. Therefore B could deduce that he was 3 if C was 1.

C in reasoning through all of this, knows that he must be 5 and not 1.

This was hard. I don't blame anyone for not trying, perhaps I should have given the numbers and had people work out why they were what they were.