Discussion
Does arc consistency guarantee a solution exists?
Answer: A
Arc consistency removes values that certainly cannot participate in a solution but does not establish that any complete assignment exists, and a problem may be arc consistent and have no solution at all. It is a necessary rather than a sufficient condition. Cycles do make the gap larger, since arc consistency is decisive for trees. A pruning technique that removes some failures and not all is still valuable, and knowing which it removes prevents it being trusted too far.
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