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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
by tobr 4y ago
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.
- hvdijk 4y agoWe are given that he says he does know and have no reason to doubt it. It is possible that Peter and Sandy know one another and already know that they are perfect at figuring out maths/logic puzzles.
- tobr 4y agoI would phrase the puzzle differently. They both need to say they know, otherwise we have no reason to believe Sandy has figured it out. And they both need to be right, which we also have no reason to believe at the moment.
- hvdijk 4y agoThe puzzle doesn't state whether Sandy has figured it out because that information is not necessary to figure out the solution. We can infer that she has (under that implicit assumption that she is a perfect logician) by the fact that we know less than she does and still have enough information, though. As for that last part: we also don't truly know that Peter isn't lying just to mess with the puzzle, I guess. That is another implicit assumption.
- bertil 4y agoIt’s generally presented as both of them being experienced mathematicians who have been doing it for a while, that they have access to a notebook and a calculator and recently (I’ve seen those since the 1980s) to a computer.