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The interestingness of a problem like this comes from its relatedness to other concepts in mathematics. The problems that are of interest are those whose solutions might contain concepts or truths that can be relevant to other fields of math. So a good math problem is not only something that is solvable and can lead to insightful truths about math, but also something that isn't too arbitrary or separated from the *rest* of math.

Take the first question; it is about proving that the sequence of the central column isn't periodic. Whatever solution may come forth might also be relevant when proving or evaluating things related to prime numbers, which are equally a human construction based on a very simple rule, get equally complex equally fast, and are often looked at in terms of series of numbers. It may turn out to be a dead end, but it also may not, and the solution to this problem might just turn out to be transferrable to another set of problems.