I understand it’s a puzzle and it requires some suspension of disbelief, but I think Peter is wrong. He doesn’t know the numbers after 14 tries. He is assuming that Sandy has figured out the trick and is able to correctly keep track of 9801 + 198 = 9999 lists of number pairs in her head. As far as I can tell by how the puzzle is phrased, that’s a totally unreasonable assumption. It’s more likely that she says “I don’t know” because she has no idea how to approach the problem, and the fact that that is even possible means that Peter is not really getting any information from her at all.