The minimum remaining values heuristic chooses an unassigned variable with the smallest current legal domain during constraint search. It tries the most constrained choice first: a domain of size zero proves failure, and size one forces a value. If one variable has two remaining digits and another has seven, the first is selected, with a separate rule for ties. This can expose contradictions earlier but does not guarantee a minimum search tree. The heuristic depends on domains after the chosen propagation method, not simply on each variable's original domain size.
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