That the other person is following the same system as them to decide whether they "know the numbers". It would be super easy for one of them to say they don't know for some other reason, in which the others' reasoning would be false.
This is what I thought. Two unstated (but implied) parts of the puzzle are that they can’t tell each other the numbers outright, and that they can only share information in yes/no format. But since they have clearly already agreed on a system beforehand, they could have also encoded the digits in binary or something.
So each person could have been sharing one binary digit of their number with each round. Or they might have used a completely different encoding. We simply cannot know.
