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Awesome game. I agree that left click to rotate left and right click to rotate right would be so much more convenient.

Change cursor to match rotation icon.

Shift click wouldn't work on mobile. Imho, just make 3 rotations in a row count as 1

This would break the game. You can always guess for free.

Not really? It's not free, it costs 1 to do 3 or 1 rotation, and it costs 2 to do 2 rotations. There is still a challenge because it's still the combination of multiple tiles that makes the full image, you don't necessarily gain information from doing 1 vs 3 rotations if the neighboring pieces aren't already correct