Oh, I'm not sure what's the problem you have. "no extra hats allowed" is an important bit. You can't solve the first level with two hats for example. There are two ways to solve this level: you can enter the hat, or rabbit can enter it.
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Yeah, I think the game is good but it's a bit buggy and poorly optimized. I got random freezes time to time, but I was able to almost finish it (96% and I can't play further because loading time is abysmal at the later stages).
Also I don't think player allowed to ride this thing all around the map: