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I'm pretty sure level 30 is uniquely solvable. Have you found a valid solution other than the one below?

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Can't make a congratulation without breaking a few eggs.

If this is called "Klein" because of Klein bottles, I'll have to say that this isn't a Klein bottle. On a Klein bottle, only one of the sides would flip you.

This game takes place on a projective plane (ℝP²). Notably, the fundamental group only has two elements whereas the fundamental group of a Klein bottle is infinite.

Also, I've just realised that I probably beat level 17 in an unintended way. I beat it while dead.

If you press Esc on level 0, it's still marked as completed.

In level 11, you can walk on water.

Level 16 doesn't have the white boundary.

Is there a way to reset the level?

Well, this was unexpected. Is there a way to reset the level?