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Comment by kenjackson | Hacker News Reader

So now, how many ways can this be done? No, it's not five. And no, it's not six either.

An infinite number of ways this can be done.

Yes, but there's more that you can say. In particular, there is more than one infinite family. How many are there? And do all solutions belong to an infinite family? Or are there isolates/sporadics?

Can you characterise the solutions? How many pieces do they contain? Some solutions have two pieces. Some have four. Are there other possibilities?

I don't know what an infinite family, isolate, or sporadic is. A quick Google search didn't make it obvious.

I think 8 pieces also works, but I think that may be it.

An infinite family seems to refer to an infinite collection of solutions that are all related in some sense. An isolate or sporadic solution is a solution that is unique and unrelated to other solutions. They are both terms used to categorize solutions.

Thanks nocipher for the definitions. From this I see no sporadics. And two infinite families, at least how I'd classify a family.

nocipher's definition are correct.

And I have, so far, 5 infinite families with, respectively, 2, 4, 8, 16 and 32 pieces.

But details matter, and you might start to question what it really means when I say "piece." Does the definition I've given really capture your intuition?

But I need to go back to writing the article.

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