Part of the problem here is that the situation presented is an extremely unusual one. Unless scientist B’s theory is deliberately idiotic, experiment 21 has to strike at a point of contention between two theories which otherwise agree, and it has to be the only experiment out of 21 which does so. On top of that, both scientists have to pick one of these theories, and they have to pick different ones. Even if those theories are the only ones which make any sense, and they’re equally likely from the available data, your chance of ending up in the situation the problem presents is less than 1⁄100.
Even if you’re given 21 data points that follow a pattern which could be predicted from the first 10, and you have to deliberately come up with a theory that fits the first 20 but not the 21st, it’s quite tricky to do so. I would be surprised if anyone could come up with even a single example of the situation presented in this puzzle (or an analogous one with even more experiments) ever occurring in the real world.
Unless experiment 21 is of a different nature than experiments 1-20. A different level of precision, say. Then I’d go with scientist B, because with more data he can make a model that’s more precise, and if precision suddenly matters a lot more, it’s easy to see how he could be right and A could be wrong.
Part of the problem here is that the situation presented is an extremely unusual one. Unless scientist B’s theory is deliberately idiotic, experiment 21 has to strike at a point of contention between two theories which otherwise agree, and it has to be the only experiment out of 21 which does so. On top of that, both scientists have to pick one of these theories, and they have to pick different ones. Even if those theories are the only ones which make any sense, and they’re equally likely from the available data, your chance of ending up in the situation the problem presents is less than 1⁄100.
Even if you’re given 21 data points that follow a pattern which could be predicted from the first 10, and you have to deliberately come up with a theory that fits the first 20 but not the 21st, it’s quite tricky to do so. I would be surprised if anyone could come up with even a single example of the situation presented in this puzzle (or an analogous one with even more experiments) ever occurring in the real world.
Unless experiment 21 is of a different nature than experiments 1-20. A different level of precision, say. Then I’d go with scientist B, because with more data he can make a model that’s more precise, and if precision suddenly matters a lot more, it’s easy to see how he could be right and A could be wrong.