Arnold's puzzle is based on open mathematical problems in combinatorial geometry. Related topics:
Given a small number of lines, one can solve the puzzle by randomly trying. As the number of lines increases, the complexity of the game grows not only quantitatively (you have to go longer to the goal), but also qualitatively: you have to invent new techniques and approaches because the old ones are not enough.
The game feels like a jigsaw puzzle, each piece of which fits any other piece, but the overall picture does not add up.