Arnold's Puzzle: From Combinatorial Geometry to a Browser Toy

Imagine a game that follows simple rules:

I have already programmed the browser toy with these rules . In the simplest case of 5 lines, the game process looks like this:

  1. Several lines are drawn on the plane, each pair of lines intersects at one point.

  2. The lines divide the plane into checkerboard-colored areas.

  3. You can rearrange the partition by collapsing and inverting the triangles.

  4. Your goal is to get as many dark areas as possible.

An example of passing a level of 5 lines
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