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A Chess problem should have a unique solution, though this criteria is not absolute. In order of severity as flaws in the problem, non-unique solutions are cooks (worst), serious duals, and harmless duals. In problem competitions, the first two tend to be disqulified and the last accepted but such a problem would be unlikely to win a prize.
Very good definition of these terms <a href='http://www.sahovski.com/PRODUCTS/OTHER/ACP/acp.htm'>here.</a>