Inference Answer

This problem can be solved by speculating what others would speculate.

If both A and B had a red ball behind him, C would instantly report that he has a black ball behind him.

If only A had a red ball behind him, B would know soon that he has a black ball, because if he didn't, C would instantly report that he has a black ball behind him.

Because nobody reports anything, everyone must have a black ball.

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