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I got to level 20 or so and had figured out a working algorithm for two cuts whereby you would cut off 1 in the first cut and then find a good angled second cut to split off all the remaining pairs. This got a little more complicated when it went up to 3 cuts though...

There has got to be some math theorem to generalize a solution to n swipes.

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https://mathworld.wolfram.com/PlaneDivisionbyLines.html might be related.

I think it got really complicated when the initial shape was not convex. If its convex initially,then at best you can split all the groups in two, and in most of the puzzles you had to split all the groups in half (possibly not evenly if the group is odd) because you the number of lines you were allowed to make was roughly ceil(log_2) the number of dots.

But when its not convex you can potentially do better than just splitting all groups in half, and i found those the most challenging levels (i think it was either 20 or 21 that was like that)

I had the impression that the optimal swipes had an equal amount of dots on either side with the swipe going across as many open gaps (edges) of the shape as possible.

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