Least Constraining Value (LCV)

After a cell is selected, LCV tries first the digit that removes the fewest candidates from its peers.

r1c15r1c23r1c3r1c4r1c57r1c6r1c7r1c8r1c9
r2c16r2c2r2c3r2c41r2c59r2c65r2c7r2c8r2c9
r3c1r3c29r3c38r3c4r3c5r3c6r3c7r3c86r3c9
r4c18r4c2r4c3r4c4r4c56r4c6r4c7r4c8r4c93
r5c14r5c2r5c3r5c48r5c5r5c63r5c7r5c8r5c91
r6c17r6c2r6c3r6c4r6c52r6c6r6c7r6c8r6c96
r7c1r7c26r7c3r7c4r7c5r7c6r7c72r7c88r7c9
r8c1r8c2r8c3r8c44r8c51r8c69r8c7r8c8r8c95
r9c1r9c2r9c3r9c4r9c58r9c6r9c7r9c87r9c99

Example for r1c3

Initially D(r1c3)={1,2,4}. Counting unassigned peers that currently contain each digit gives this simple estimate:

Trial valuePeer domains losing that value
17
48
211

LCV therefore tries 1 first, then 4, then 2. These counts change after propagation, so a solver normally computes them from the current state.

MRV versus LCV

MRV deliberately chooses a difficult variable; LCV then chooses the value that preserves the most freedom for remaining variables.

Exercise: Recompute these counts after assigning and propagating r5c5=5. Does the value order change?