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A bloke I met at a car boot sale told me that any scramble could be solved in 48 moves. He also claimed to have solved a cube by accident.
To be fair, I've seen one person sort of solve by accident: he was able to do a side but no more; halfway through he noticed he got to a stage when he had only ~6 moves left and did that intuitively. Props to him for having the spatial recognition and reasoning for that, especially since he didn't even know how to solve the cube.