Sudoku technique · Candidate elimination

Hidden Pair

A Hidden Pair appears when two digits can occur in only the same two cells of a row, column, or box, even though those cells show other candidates.

Topic role
Candidate-elimination proof
Engine rank
Rank 5
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Learning order

Topic relationships

These links express the same learning and proof relationships used throughout the library.

Verified example

Work through the example

Hidden Pair · Verified example
R1C1: given 1
R1C2: given 2
R1C3: given 3
R1C4: given 4
R1C5: given 5
R1C6: empty
R1C7: given 7
R1C8: empty
R1C9: empty
R2C1: given 4
R2C2: given 5
R2C3: given 6
R2C4: given 7
R2C5: empty
R2C6: empty
R2C7: given 1
R2C8: empty
R2C9: given 3
R3C1: given 7
R3C2: given 8
R3C3: given 9
R3C4: empty
R3C5: empty
R3C6: empty
R3C7: empty
R3C8: empty
R3C9: empty
R4C1: empty
R4C2: given 3
R4C3: given 4
R4C4: given 5
R4C5: empty
R4C6: given 7
R4C7: empty
R4C8: empty
R4C9: empty
R5C1: given 5
R5C2: given 6
R5C3: given 7
R5C4: given 8
R5C5: given 9
R5C6: given 1
R5C7: empty
R5C8: empty
R5C9: given 4
R6C1: empty
R6C2: given 9
R6C3: given 1
R6C4: empty
R6C5: empty
R6C6: empty
R6C7: given 5
R6C8: empty
R6C9: given 7
R7C1: given 3
R7C2: given 4
R7C3: given 5
R7C4: empty
R7C5: given 7
R7C6: empty
R7C7: empty
R7C8: empty
R7C9: given 2
R8C1: given 6
R8C2: given 7
R8C3: given 8
R8C4: empty
R8C5: empty
R8C6: empty
R8C7: empty; pattern cell; Before 3, 4
R8C8: empty; pattern cell; candidate deletion 1, 5, 9; Before 1, 3, 4, 5, 9; After 3, 4
R8C9: empty
R9C1: given 9
R9C2: given 1
R9C3: given 2
R9C4: given 3
R9C5: empty
R9C6: empty
R9C7: given 6
R9C8: given 7
R9C9: empty

Pattern cells: R8C7, R8C8. Remove 1, 5, 9 from R8C8.

Pattern cells
R8C7, R8C8
Pattern digits
3, 4
Reviewed unit
Row 8

Exact candidate changes

  • Remove 1, 5, 9 from R8C8Before: 1, 3, 4, 5, 9After: 3, 4
  1. Choose one unit and count the candidate positions for each missing digit.
  2. Find two digits whose only positions are the same two cells.
  3. Reserve those cells for the two digits without deciding their order.
  4. Remove every non-pair candidate from the two pattern cells.

Fixed practice

Count where each digit can go in one unit; compare location pairs rather than candidate-list lengths.

Fixed practice · R2C8
Hidden Pair · Fixed practice
R1C1: given 1
R1C2: empty
R1C3: given 3
R1C4: given 4
R1C5: empty
R1C6: given 6
R1C7: empty
R1C8: given 8
R1C9: given 9
R2C1: empty
R2C2: empty
R2C3: empty
R2C4: empty
R2C5: empty
R2C6: given 9
R2C7: given 1
R2C8: empty; pattern cell; candidate deletion 4, 7; Before 2, 3, 4, 7; After 2, 3
R2C9: empty
R3C1: empty
R3C2: given 8
R3C3: empty
R3C4: given 1
R3C5: empty
R3C6: given 3
R3C7: empty
R3C8: given 5
R3C9: given 6
R4C1: empty
R4C2: empty
R4C3: given 4
R4C4: empty
R4C5: given 6
R4C6: empty
R4C7: empty
R4C8: given 9
R4C9: empty
R5C1: given 5
R5C2: empty
R5C3: given 7
R5C4: empty
R5C5: empty
R5C6: empty
R5C7: empty
R5C8: empty; pattern cell; candidate deletion 4, 6; Before 2, 3, 4, 6; After 2, 3
R5C9: empty
R6C1: empty
R6C2: empty
R6C3: empty
R6C4: given 2
R6C5: given 3
R6C6: empty
R6C7: empty
R6C8: empty
R6C9: given 7
R7C1: given 3
R7C2: given 4
R7C3: given 5
R7C4: given 6
R7C5: empty
R7C6: empty
R7C7: empty
R7C8: given 1
R7C9: given 2
R8C1: empty
R8C2: empty
R8C3: empty
R8C4: empty
R8C5: empty
R8C6: empty
R8C7: given 3
R8C8: empty
R8C9: empty
R9C1: empty
R9C2: empty
R9C3: empty
R9C4: given 3
R9C5: given 4
R9C6: empty
R9C7: empty
R9C8: empty
R9C9: given 8

Pattern cells: R2C8, R5C8. Remove 4, 7 from R2C8; Remove 4, 6 from R5C8.

Pattern cells
R2C8, R5C8
Pattern digits
2, 3
Reviewed unit
Column 8

Exact candidate changes

  • Remove 4, 7 from R2C8Before: 2, 3, 4, 7After: 2, 3
  • Remove 4, 6 from R5C8Before: 2, 3, 4, 6After: 2, 3

Common mistakes

Common mistakes

Looking only for cells with two candidates; Hidden Pairs are found by counting digit positions.

Removing the pair digits from other cells instead of removing extra digits from the pair cells.

Review information

What is verified here

The independent verifier recomputes both digits’ only positions, the two exact pattern cells, and every non-pair candidate removed from those cells.

Fixture ID
p3b-hidden-pair-row-01 / p3b-hidden-pair-column-01
Engine version
legen-sudoku-engine/1.3.0
Verification status
Independent candidate-elimination verifier passed
Facts reviewed
2026-07-18
Technique terminology and examples are tied to the published engine version. See the review information below for scope and dates.