> Your problem here is that if A saw 13, they would conclude that B saw 7 or 5. If A saw 14, they would conclude that B saw 4 or 6. In no case can A guess immediately.
The common knowledge at this point is that B sees between 6 and 10, so A knows B doesn’t see 5 or 4.
Your definition of common knowledge (they both know it and they both know the other knows it too) is too weak. For something to be truly common knowledge, the knowledge needs to be nested arbitrarily deep (they know, they know they know, (they know)^3, ...). Otherwise there's some remaining uncertainty about whether the other knows the common knowledge.
In particular, your assumption that if A saw 14 they'd know that B doesn't see 5 or 4 is wrong, because if A saw 14 they don't have the common knowledge that B sees between 6 and 10, because that's dependent on A seeing 12.
The common knowledge at this point is that B sees between 6 and 10, so A knows B doesn’t see 5 or 4.