Medium Sudoku Techniques

Medium puzzles provide 30–37 given cells — fewer clues than easy, and arranged so that pure cross-hatching and naked singles are not always available from the start. You will need two additional techniques: hidden singles and locked candidates (also called pointing pairs or box-line reduction). Pencil marks — writing candidate lists in every empty cell — become genuinely necessary rather than optional.

The good news: every medium Sudoku has a unique solution reachable by logic alone. No guessing is ever required. If you feel stuck, one of the techniques in this guide will unlock the next move.

A hidden single is a cell that is the only possible location for a specific digit within a row, column, or 3×3 box — even though that cell still has multiple candidates. The digit is "hidden" among those candidates.

The conceptual shift: naked singles ask "Which numbers can go in this cell?" Hidden singles ask "Where in this group can this number go?" These are complementary perspectives on the same constraint.

Finding hidden singles step by step:

1. Pick a digit — say, 7.
2. Look at a row. For every empty cell in that row, check whether 7 is a valid candidate (not already present in the cell's column or box).
3. If only one empty cell in the row can legally hold 7, place it. That is a hidden single.
4. Repeat for each column and each 3×3 box.

Column 5 — candidates per empty row cell:

  Row 1: {2, 5, 9}
  Row 2: {3, 5}
  Row 3: {1, 5, 7}    ← 7 appears here and nowhere else in this column
  Row 4: {2, 3}
  Row 5: {2, 5, 8}
  Row 6: {3, 5}
  Row 7: {2, 5}
  Row 8: {2, 5}
  Row 9: {2, 5}
  (rows 4 and 6 are given cells, omitted)

→ 7 only appears as a candidate in row 3.
  Place 7 at (row 3, col 5) — hidden single confirmed.

Sometimes a candidate digit within a 3×3 box is only possible in cells that all lie on the same row or column. When that happens, the digit must land in that row or column — somewhere inside the box. You can therefore eliminate that digit from all other cells of that row or column that lie outside the box.

This technique is called locked candidates (or pointing pairs/triples, depending on whether two or three cells are involved).

Step by step:

1. Pick a box and a digit not yet placed in it.
2. List every cell in the box where that digit is still a candidate.
3. If all those cells lie in a single row — or a single column — the digit is locked to that line within the box.
4. Eliminate the digit from every other empty cell on the same row or column that lies outside the box.

Top-right box (rows 1–3, cols 7–9) — scanning for digit 4:

  (1,7): 4 is impossible — row 1 already has 4
  (1,8): 4 is impossible — row 1 already has 4
  (1,9): 4 is impossible — row 1 already has 4
  (2,7): 4 is impossible — row 2 already has 4
  (2,8): 4 is impossible — row 2 already has 4
  (2,9): 4 is impossible — row 2 already has 4
  (3,7): 4 is a candidate ✓
  (3,8): 4 is a candidate ✓
  (3,9): 4 is impossible — col 9 already has 4

All 4-candidates in this box land on row 3.
→ Eliminate 4 from every other empty cell in row 3 outside this box
  (cells in cols 1–6 that still list 4 as a candidate).

Locked candidates do not directly place a digit — they eliminate candidates, which may expose hidden or naked singles elsewhere in the row or column.

Box-line reduction is the mirror of locked candidates. If a candidate digit in a row (or column) only appears inside one specific 3×3 box — nowhere else in that row — then that digit must land somewhere in that box on that row. You can eliminate the digit from other cells in the same box that are not on the target row.

How to apply it:

• Scan a row for a digit. Note every empty cell in the row that still lists the digit as a candidate.
• If all those cells fall within one 3×3 box, the digit is box-locked on this row.
• Eliminate the digit from every other cell in that box (cells not on this row).

Box-line reduction and locked candidates are logically equivalent but look at the puzzle from opposite directions. Together they handle the majority of medium-puzzle eliminations.

At medium difficulty, pencil marks are not optional — they are the right tool. Here is a disciplined workflow:

1. Seed the board first: Before filling in candidates, apply all visible naked singles and last-remaining-cell moves. This reduces clutter.
2. Mark every empty cell: Go cell by cell and write the candidates based on row, column, and box elimination. Be complete — a missing candidate hides a valid move.
3. Apply hidden singles: For each row, column, and box, check whether any digit appears in only one cell's candidate list.
4. Apply locked candidates: Scan each box for digits whose candidates align on a single row or column.
5. Update after every placement: Remove the placed digit from candidate lists of all cells in the same row, column, and box. Then search again from step 3.

The discipline of maintaining accurate candidate lists is what separates fast, reliable solvers from people who "get stuck" on medium. The technique is not hard — it just requires consistency.

If no move appears after a full scan, try these in order before reconsidering your approach:

• Re-check every row, column, and box for hidden singles. It is easy to miss one on the first pass, especially in nearly-full groups.
• Look for locked candidates in boxes that changed recently. New placements may have confined a digit to a single row or column within a box that was previously spread across two.
• Verify your pencil marks. One incorrect or missing candidate can conceal a logical move. Re-derive the candidates for a few suspect cells.
• Re-apply box-line reduction to rows and columns you have not recently checked.

Medium puzzles are always solvable without guessing. If you exhaust this list and find nothing, the most likely explanation is a pencil-mark error earlier. Use undo to backtrack to before the likely error.

Run through this list after every placement. Most medium puzzles yield to repeated passes of these five checks:

• Any cell with only one candidate? → Naked single — place it.
• Any digit that fits in only one cell within a row, column, or box? → Hidden single — place it.
• Any digit in a box confined to a single row or column? → Locked candidates — eliminate outside the box.
• Any digit in a row/column confined to one box? → Box-line reduction — eliminate within the box.
• Any group with only one empty cell? → Last remaining — place it immediately.

Check this list in order after every placement. The pattern recognition becomes fast with practice — within a few weeks, your eye will spot hidden singles and locked candidates without consciously running the checklist.