Locked Candidates in Sudoku: Pointing Pairs & Box-Line Reductions

What Are Locked Candidates?

When you advance from beginner to intermediate or expert Sudoku puzzles, singles alone are no longer enough. You need candidate eliminations to unlock the board.

Locked Candidates (also known as Intersections) happen when the possible spots for a number in one unit are constrained in a way that affects an intersecting unit. There are two complementary types:

1. Type 1: Pointing Pair / Triple (Box to Line): Inside a 3×3 box, all candidates for a digit lie strictly along a single row or column. Therefore, that digit must be placed on that line inside this box—and cannot appear anywhere else in that row or column outside the box!
2. Type 2: Box-Line Reduction (Line to Box): Along a row or column, all candidates for a digit lie strictly within a single 3×3 box. Therefore, that digit cannot appear in any other cell of that 3×3 box!

Worked Example: Pointing Pair of 7s in Box 2 Eliminates 7 at R2C7

Look at Box 2 (top-middle, Rows 1–3, Columns 4–6) on the board below. Box 2 already contains 1, 2, 3, 4, 5, 8 and is missing {6, 7, 9} across three empty cells (R1C5, R2C4, and R2C5):

• Row 1 (R1C5): Blocked from holding 7 by the given 7 at Row 1, Column 2 (R1C2).
• Row 2 (R2C4 and R2C5): Neither Column 4 nor Column 5 contains a 7 yet, so inside Box 2, candidate 7 is restricted strictly to R2C4 and R2C5 (a Pointing Pair along Row 2).
• Elimination in Box 3 (R2C7): Follow Row 2 rightwards into Box 3. Cell Row 2, Column 7 (R2C7) sees 1, 2, 3, 4, 5, 6, 8 in its peers, leaving candidates {7, 9}. Because Box 2 claims Row 2's 7, candidate 7 is eliminated from R2C7, leaving 9 as the sole survivor!