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Bumping my offer for variant counting threads to the top of the new page. I’ll treat it as a no if no one expresses interest by the time this page is finished.

Would anyone be interested in either of the following counting threads? I’d make the OP to provide some examples, as the rules are best described by example.

¹ Cyclicly-increasing bases also work, but decreasing allows for a better OP example to show the pattern.

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While it’s a cool idea PUBLIQ, at the same time, it would be kinda confusing, even if you would explain the rules.

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Fair points. When I’ve seen them run elsewhere, the rational numbers thread is the one that often gets off track first.

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I’ll give examples for each. Each bullet point is a separate post.

It’s a zigzag path through the rational numbers (that’s how you prove they have the same cardinality as the natural numbers we’re counting in this thread).
Each poster continues until they hit a non-reducible fraction that does not have 1 as either the numerator or denominator. Once a fraction with a 1 is reached, the other part of the fraction is incremented by 1 and then the pattern starts to head toward putting the 1 in the other slot while keeping the same sum of numerator and denominator.

Cycling bases in the other direction wouldn’t show how this differs from plain counting until post 16.

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