Minimum Remaining Values (MRV)

MRV selects the unassigned cell with the fewest remaining candidates—the fail-first strategy.

r1c15r1c23r1c3r1c4r1c57r1c6r1c7r1c8r1c9
r2c16r2c2r2c3r2c41r2c59r2c65r2c7r2c8r2c9
r3c1r3c29r3c38r3c4r3c5r3c6r3c7r3c86r3c9
r4c18r4c2r4c3r4c4r4c56r4c6r4c7r4c8r4c93
r5c14r5c2r5c3r5c48r5c5r5c63r5c7r5c8r5c91
r6c17r6c2r6c3r6c4r6c52r6c6r6c7r6c8r6c96
r7c1r7c26r7c3r7c4r7c5r7c6r7c72r7c88r7c9
r8c1r8c2r8c3r8c44r8c51r8c69r8c7r8c8r8c95
r9c1r9c2r9c3r9c4r9c58r9c6r9c7r9c87r9c99

Candidate comparison

CellInitial reduced domain
r1c3{1,2,4}
r1c4{2,6}
r5c5{5}
r7c6{7}
r7c9{4}
r8c8{3}

MRV chooses a singleton before branching. Assigning forced cells may create additional singletons, allowing substantial progress without guessing.

Why fail first?

If a cell has no legal value, the current branch is already impossible. If it has one value, delaying it provides no benefit. Handling the most constrained cells first exposes contradictions early.

Exercise: After assigning r5c5=5 and propagating, which new singleton cells appear immediately?