Another serious problem is that the students must make the necessary assumption that the rule be simple. In the context of school, simple is generally “most trivial to figure out”.
This is a necessary assumption because there could be rules that would not be possible to determine by guessing. For example, you’d have to spend the lifetime of the universe guessing triplets to correctly identify that the rule is “Ascending integers except sequences containing the 22nd Busy Beaver number”, and then you still wouldn’t know if there’s some other rider.
If it was said, “It will require several more guesses to figure out the rule, but not more than a couple dozen, and the sequences you have don’t fully tell you what the rule is”, the exercise would be a lot more sane. At worst, the only mistake the students made was assuming that the exercise was supposed to be too simple. Which is like asking them to be mind readers: I’m thinking of a problem; on a scale of 1-10, please guess how difficult it is to solve.
Another serious problem is that the students must make the necessary assumption that the rule be simple. In the context of school, simple is generally “most trivial to figure out”.
This is a necessary assumption because there could be rules that would not be possible to determine by guessing. For example, you’d have to spend the lifetime of the universe guessing triplets to correctly identify that the rule is “Ascending integers except sequences containing the 22nd Busy Beaver number”, and then you still wouldn’t know if there’s some other rider.
If it was said, “It will require several more guesses to figure out the rule, but not more than a couple dozen, and the sequences you have don’t fully tell you what the rule is”, the exercise would be a lot more sane. At worst, the only mistake the students made was assuming that the exercise was supposed to be too simple. Which is like asking them to be mind readers: I’m thinking of a problem; on a scale of 1-10, please guess how difficult it is to solve.