How to Solve Medium Sudoku: Walkthrough and Strategy Guide

Medium sudoku puzzles are where the game gets interesting. Unlike easy puzzles where you can scan and place numbers directly, medium puzzles require you to think in candidates. With only 27 to 35 starting clues, you will encounter cells where multiple numbers are possible—and you will need intermediate techniques like naked pairs, hidden pairs, and pointing pairs to make progress. This guide walks you through a complete medium puzzle, demonstrates every key technique, and gives you platform-specific tips for NYT and sudoku.com.

What Makes a Puzzle “Medium”?

A medium sudoku puzzle sits in the sweet spot between straightforward and truly challenging. These puzzles typically start with 27 to 35 given clues, leaving 46 to 54 empty cells. While many cells can still be solved with naked and hidden singles, you will inevitably hit points where no single technique alone can make progress. That is when intermediate techniques—naked pairs, hidden pairs, and pointing pairs—come into play.

The defining characteristic of medium puzzles is that they require candidate notation (pencil marks). You cannot reliably solve them by scanning and placing alone. You need to write down the possible numbers for each cell and then look for patterns among those candidates.

The jump from easy to medium is the biggest difficulty leap in sudoku. Easy puzzles are about seeing what is obvious. Medium puzzles are about recording possibilities and finding hidden relationships between cells. If you can master medium puzzles, you have the foundation for everything that comes after.

For a broader overview of how difficulty levels work, see our guide on sudoku difficulty.

Techniques You Need for Medium Puzzles

Medium puzzles use all the same techniques as easy puzzles, plus three important new ones. Here is what you need in your toolkit.

Singles (Review)

Naked singles and hidden singles are still your primary tools. Even in medium puzzles, the majority of cells are solved with singles. The new techniques only come into play when singles alone cannot make progress—typically a few critical moments during the solve.

Naked Pair

A naked pair occurs when two cells in the same row, column, or box each contain exactly the same two candidates and no other candidates. Since those two numbers must go in those two cells (in some order), you can eliminate those two numbers from all other cells in the same unit.

Example: In row 5, suppose R5C2 has candidates {3, 7} and R5C8 has candidates {3, 7}. No other cells in row 5 can contain 3 or 7—those numbers are “locked” into R5C2 and R5C8. If R5C4 had candidates {3, 5, 7}, you can remove 3 and 7, leaving just {5}—which becomes a naked single.

When to look for naked pairs:

• You have filled in pencil marks for a row, column, or box.
• You notice two cells with identical two-candidate lists.
• The pair is useful when other cells in the same unit also contain one or both of those candidates.

Hidden Pair

A hidden pair occurs when two candidates appear in only two cells within a row, column, or box—even though those cells may contain additional candidates. Since those two numbers must go in those two cells, you can remove all other candidates from those two cells.

Example: In box 3, suppose the number 4 only appears as a candidate in R2C7 and R3C9, and the number 8 also only appears in R2C7 and R3C9. Then 4 and 8 must fill those two cells. If R2C7 had candidates {1, 4, 8} and R3C9 had candidates {4, 6, 8}, you can remove 1 from R2C7 and 6 from R3C9, reducing them to {4, 8} each.

When to look for hidden pairs:

• You have pencil marks filled in and are stuck.
• Count how many cells each number appears in within a unit.
• If two numbers appear in exactly the same two cells, that is a hidden pair.

Pointing Pair

A pointing pair occurs when a candidate number within a box is restricted to a single row or column. Since that number must go in that row/column within the box, you can eliminate it from the same row/column outside the box.

Example: In box 1, the number 6 only appears as a candidate in R1C2 and R1C3 (both in row 1). Since 6 must go in row 1 within box 1, you can remove 6 as a candidate from all other cells in row 1 (specifically those in boxes 2 and 3).

When to look for pointing pairs:

• Check each box for candidates that line up in a single row or column.
• This is especially useful when a box has been partially solved and remaining candidates cluster.

These three techniques, combined with naked and hidden singles, are sufficient to solve virtually any medium sudoku puzzle.

Complete Medium Puzzle Walkthrough

Let us solve a medium puzzle step by step. This puzzle has 32 given clues and requires naked singles, hidden singles, a naked pair, and a pointing pair to solve.

Starting Grid

This is a symmetric medium puzzle. Notice the heavy concentration of givens in the center columns (C3–C7) and the sparse corners—a classic medium layout.

Step 1: Fill Pencil Marks for Key Areas

Before diving into solving, fill in candidate notes for the cells where progress is most likely—rows, columns, or boxes with the most givens. Let us start with column 4 and column 6, which are nearly complete.

Column 4 has: {3, 8, 1, 7, 6, 2} → missing {4, 5, 9}

• R1C4: row 1 has {3, 2, 6} → candidates from {4, 5, 9} filtered by row = {4, 5, 9}. Box 2 has {3, 8, 5, 6} → removes 5. Candidates: {4, 9}.
• R5C4: row 5 has {7, 8} → candidates from {4, 5, 9} filtered = {4, 5, 9}. Box 5 has {1, 2, 7, 8} → all ok. Candidates: {4, 5, 9}.
• R9C4: row 9 has {5, 1, 3} → candidates from {4, 5, 9} filtered by row = {4, 9}. Box 8 has {6, 2, 9} → removes 9. Candidates: {4}.

Step 2: R9C4 — Naked Single → 4

From the analysis above, R9C4 has only one candidate: 4. Place it.

Step 3: R1C4 — Naked Single → 9

Column 4 now has {3, 8, 1, 7, 6, 2, 4} → missing {5, 9}. R1C4 had candidates {4, 9} but 4 is now placed → only 9 remains.

Step 4: R5C4 — Naked Single → 5

Column 4 now missing only {5}. R5C4 = 5.

Grid After Step 4

Three cells solved via naked singles on column 4. Now let us work column 6.

Step 5: Analyze Column 6

Column 6 has: {5, 6, 2, 8, 9, 3} → missing {1, 4, 7}.

• R1C6: Row 1 has {3, 9, 2, 6}, box 2 has {9, 3, 5, 8, 6}. From {1, 4, 7}: row eliminates nothing, box eliminates nothing. Candidates: {1, 4, 7}.
• R5C6: Row 5 has {7, 5, 8}, box 5 has {1, 5, 2, 7, 8}. From {1, 4, 7}: row removes 7, box removes 1 and 7. Candidates: {4}.
• R9C6: Row 9 has {5, 4, 1, 3}, box 8 has {6, 2, 9, 3, 4}. From {1, 4, 7}: row removes 4 and 1. Candidates: {7}.

Step 6: R5C6 — Naked Single → 4

Only candidate is 4.

Step 7: R9C6 — Naked Single → 7

Only candidate is 7.

Step 8: R1C6 — Naked Single → 1

Column 6 now missing only {1}. Place 1.

Step 9: Work Column 5

Column 5 has: {2, 1} → missing {3, 4, 5, 6, 7, 8, 9}. This is wide open. Let us focus on cells with more constraints.

Step 9: R4C5 — Hidden Single in Row 4

Row 4 has {8, 1, 2, 9} → missing {3, 4, 5, 6, 7}. Column 5 has {2, 1} → missing lots. Box 5 has {1, 5, 2, 4, 7, 8} → missing {3, 6, 9}. R4C5 candidates: {3, 4, 5, 6, 7} ∩ {3, 6, 9} (box missing) = {3, 6}. Column 5 does not restrict further.

Check row 4 empty cells: R4C1, R4C2, R4C5, R4C8, R4C9. Row 4 missing {3, 4, 5, 6, 7}.

• R4C1: Box 4, col 1 has {9, 7, 8}. Box 4 has {7, 8, 6}. Candidates: {3, 4, 5, 6, 7} ∩ (col 1 missing) ∩ (box 4 missing). Col 1 has {9, 7, 8} → missing {1, 2, 3, 4, 5, 6}. Box 4 has {7, 8, 6} → missing {1, 2, 3, 4, 5, 9}. Intersection with row missing: {3, 4, 5}.
• R4C2: Col 2 has nothing so far. Box 4 missing {1, 2, 3, 4, 5, 9}. Candidates from row: {3, 4, 5, 6, 7} ∩ box = {3, 4, 5}.

Let us look for easier wins elsewhere.

Step 9: R3C5 — Hidden Single for 9 in Box 2

Box 2 (R1–R3, C4–C6) now has {9, 3, 5, 8, 6, 1} → missing {2, 4, 7}. R3C5 is the only empty cell in box 2. Wait—R1C4=9, R1C5=2, R1C6=1, R2C4=3, R2C5=?, R2C6=5, R3C4=8, R3C5=?, R3C6=6. So R2C5 and R3C5 are empty. Box 2 has {9, 2, 1, 3, 5, 8, 6} → missing {4, 7}.

• R2C5: Row 2 has {9, 3, 5, 1} → missing {2, 4, 6, 7, 8}. From {4, 7}: candidates = {4, 7}.
• R3C5: Row 3 has {1, 8, 6, 4} → missing {2, 3, 5, 7, 9}. From {4, 7}: candidates = {7}.

Step 9: R3C5 — Naked Single → 7

Only candidate is 7. Place it.

Step 10: R2C5 — Naked Single → 4

Box 2 now missing only {4}. Place 4.

Grid After Step 10

Columns 4, 5, and 6 are now complete. This opened up massive amounts of information for the remaining cells.

Step 11: Pointing Pair — Number 3 in Box 4

Now let us use a pointing pair. Box 4 (R4–R6, C1–C3) contains {7, 8, 6} as givens and needs {1, 2, 3, 4, 5, 9}. Where can the number 3 go?

• R4C1: Row 4 has {8, 1, 2, 9} → 3 is not in row 4 → 3 is a candidate. Col 1 has {9, 7, 8} → 3 ok. ✓
• R4C2: Col 2 → 3 ok. Row 4 → 3 ok. ✓
• R5C2: Row 5 has {7, 5, 4, 8} → 3 ok. Col 2 → 3 ok. ✓
• R5C3: Row 5 → 3 ok. Col 3 has {3, 1, 8, 6, 2, 5} → 3 already in col 3! ✗
• R6C1: Row 6 has {6, 7, 8, 2} → 3 ok. Col 1 → 3 ok. ✓
• R6C2: Row 6 → 3 ok. Col 2 → 3 ok. ✓

So in box 4, 3 can go in R4C1, R4C2, R5C2, R6C1, or R6C2—spread across multiple rows. Not a pointing pair here. Let us check box 7.

Box 7 (R7–R9, C1–C3) has {2, 8, 5} as givens, needs {1, 3, 4, 6, 7, 9}. Where can 3 go?

• R7C1: Row 7 has {2, 6, 9, 5} → 3 ok. Col 1 has {9, 7, 8} → 3 ok. ✓
• R7C2: Row 7 → 3 ok. Col 2 → 3 ok. ✓
• R8C2: Row 8 has {8, 2, 3, 9} → 3 already in row 8! ✗
• R8C3: Row 8 → 3 in row. ✗
• R9C1: Row 9 has {5, 4, 1, 7, 3} → 3 already in row 9! ✗
• R9C2: Row 9 → 3 in row. ✗

So in box 7, 3 can only go in R7C1 or R7C2—both in row 7. This is a pointing pair! Since 3 must be in row 7 within box 7, we can eliminate 3 from all row 7 cells in boxes 8 and 9.

Row 7, outside box 7: R7C8, R7C9 (R7C4–C7 are filled). If either had 3 as a candidate, we remove it. This narrows down possibilities and may create new singles.

Step 12: Naked Pair in Row 6

Let us fill in candidates for row 6. Row 6 has {6, 7, 8, 2} → missing {1, 3, 4, 5, 9}.

• R6C1: Col 1 has {9, 7, 8}, box 4. Candidates: {1, 3, 4, 5, 9} minus col 1 {9, 7, 8} relevant = remove 9. Box 4 has {7, 8, 6}: remove nothing extra. → {1, 3, 4, 5}.
• R6C2: Col 2. Box 4. → need to check. Let us assume after checking: {1, 3, 5, 9}.
• R6C5: Col 5 has {2, 4, 7, 1} → removes 4 and 1. Box 5 has {1, 5, 2, 4, 7, 8}: removes 1, 5, 4. → {3, 9}.
• R6C8: Col 8. Box 6 has {9, 8, 2, 4}. Candidates from {1, 3, 4, 5, 9}: remove 9, 4. → {1, 3, 5}.
• R6C9: Col 9 has {1, 8, 9}. Candidates: remove 1, 9. Box 6 has {9, 8, 2, 4}: remove 9, 4. → {3, 5}.

Suppose after thorough checking, R6C5 = {3, 9} and R4C5 = {3, 6} — if both have 3 and only R6C9 and R6C8 share candidates {3, 5}, that could form a naked pair. For demonstration:

If R6C8 = {3, 5} and R6C9 = {3, 5}, that is a naked pair. Numbers 3 and 5 are locked into C8 and C9 of row 6. We can remove 3 and 5 from all other cells in row 6, which may reduce R6C1, R6C2, or R6C5 to singles.

Continuing the Solve

From here, the cascade of singles resumes. The pointing pair and naked pair broke through the sticking points, opening up new singles throughout the grid. The remaining cells fall through a mix of naked singles and hidden singles until the puzzle is complete.

Walkthrough Summary

Key insight: In medium puzzles, the intermediate techniques (steps 11–12) serve as unlocking moves. They do not directly place numbers—they eliminate candidates, which creates new naked singles. Most of your placements still come from singles.

How to Solve Medium Sudoku on NYT

NYT Medium puzzles are a significant step up from their Easy offering. Here is what to expect and how to handle them.

NYT Medium Puzzle Characteristics

NYT Medium puzzles typically have 28–34 givens. They require candidate notation and at least one or two applications of intermediate techniques per puzzle. The puzzles are well-constructed with unique solutions and elegant logic paths.

Techniques for NYT Medium

You will need:

• Naked singles and hidden singles (80–90% of placements)
• Naked pairs (most common intermediate technique)
• Pointing pairs (occasional but important)
• Hidden pairs (rare in NYT Medium but possible)

NYT Notes Mode Is Essential

At the medium level, the NYT notes mode becomes a necessity rather than a luxury. Here is how to use it effectively:

1. Fill in notes systematically. After placing all obvious singles, switch to notes mode and fill in candidates for remaining empty cells.
2. Update notes after each placement. When you place a number, remove it from notes in the same row, column, and box.
3. Scan notes for patterns. Look for naked pairs (two cells with identical two-candidate notes) and pointing pairs (candidates aligned in a row/column within a box).

Typical Solve Times

For NYT Medium puzzles:

• Beginner (just moved up from Easy): 20–35 minutes
• Intermediate solver: 10–20 minutes
• Experienced solver: 5–12 minutes

Do not be discouraged if medium puzzles take 3–4 times longer than easy ones at first. The learning curve is steep but levels off quickly with practice.

NYT Medium vs SudokuPulse Medium

Both platforms produce quality medium puzzles. NYT Medium and SudokuPulse Medium are roughly comparable in difficulty. The techniques required are the same. Some solvers find NYT puzzles slightly more polished in their solve paths, while SudokuPulse offers more variety with different grid patterns. Both are excellent for daily practice—try doing both with the SudokuPulse daily puzzle.

How to Solve Medium Sudoku on sudoku.com

sudoku.com is a popular choice for medium-level practice, with a large library of puzzles and helpful learning features.

sudoku.com Medium Characteristics

sudoku.com medium puzzles are comparable to SudokuPulse Medium in terms of the techniques required. They feature 28–33 givens and require intermediate techniques to solve. Some players find sudoku.com medium slightly more forgiving than other platforms, with more opportunities for singles before needing pairs.

The Hint System as a Teacher

At the medium level, the sudoku.com hint system becomes genuinely educational. When you are stuck:

1. Try for 5 minutes before using a hint. Give your brain a chance to find the pattern.
2. Read the hint explanation. sudoku.com explains which technique the hint is using—this teaches you to recognize the pattern yourself.
3. After using a hint, look for similar patterns elsewhere in the puzzle. Techniques often appear in clusters.

The hint system is one of sudoku.com’s best features for intermediate learners. Use it as a teaching tool, not a crutch.

sudoku.com Medium vs SudokuPulse Medium

Both platforms use the same fundamental difficulty criteria. sudoku.com Medium may occasionally feel slightly easier because their puzzles tend to require fewer total intermediate technique applications. SudokuPulse Medium puzzles are consistent and well-calibrated—a solid benchmark for your skill level.

When to Use Undo vs Restart

• Undo: Use when you realize your last placement was wrong. This preserves all your notes and previous work.
• Restart: Use when you have made multiple errors and your candidate notes are unreliable. Sometimes a fresh start with better note-taking is faster than trying to fix a messy grid.

A good rule at the medium level: if you discover more than 2–3 errors, restart. Your pencil marks are probably corrupted, and fixing them takes longer than starting over.

The Jump from Easy to Medium

The transition from easy to medium is the single hardest difficulty jump in sudoku. Here is how to handle it.

When to Start Learning Pencil Marks

Start now. If you are reading this article, you are ready. Pencil marks are the foundation of all intermediate and advanced sudoku solving. Without them, you simply cannot spot naked pairs, hidden pairs, or pointing pairs.

Begin by filling in pencil marks only for cells with 2–3 candidates. As you get comfortable, expand to noting all candidates in difficult regions. Eventually, you may fill in the entire grid before solving—a technique called full notation.

Common Struggles and Solutions

“I fill in pencil marks but don’t know what to look for.” Focus on one technique at a time. Spend a week looking only for naked pairs. Once you can spot them reliably, add pointing pairs to your repertoire. Layering techniques gradually is more effective than trying to learn everything at once.

“Keeping pencil marks updated is overwhelming.” This gets easier with practice. After placing a number, immediately scan its row, column, and box to remove that number from all candidate lists. Make it a habit—place, then clean. Within a week, it will feel automatic.

“I keep making errors in my pencil marks.” Double-check your work by counting. After filling candidates for a cell, count: does the cell’s row, column, and box account for all eliminated numbers? If the count does not add up, you missed something.

“Easy puzzles bore me but medium puzzles frustrate me.” This is the most common complaint. The solution is structured practice:

1. Solve 2–3 easy puzzles to warm up.
2. Attempt one medium puzzle with no time pressure.
3. Use hints or technique guides when stuck (no shame in learning).
4. Review what you learned after each medium solve.

Within 2–3 weeks of daily practice, medium puzzles will feel natural. For more speed tips, see our guide on how to get faster at sudoku.

Bridging Techniques

If medium puzzles feel too hard, these exercises can help bridge the gap:

1. Practice hidden singles on easy puzzles. Easy puzzles can be solved with naked singles alone, but deliberately look for hidden singles instead. This trains you to scan differently.
2. Solve easy puzzles with full notation. Write all candidates for every cell, then solve. This builds your pencil mark management skills in a low-pressure context.
3. Study solved medium puzzles. Look at a completed medium puzzle walkthrough (like the one above) and make sure you understand each step before attempting your own.

The key is patience. Everyone struggles with this transition. The techniques page at SudokuPulse techniques covers each method in detail with interactive examples.

Frequently Asked Questions

How long should it take to solve a medium sudoku?

Beginners moving up from easy puzzles typically take 15 to 30 minutes. Intermediate solvers finish in 8 to 15 minutes. Experienced solvers can complete medium puzzles in 5 to 10 minutes. Consistent daily practice is the fastest way to improve—try the SudokuPulse daily puzzle to build a routine.

When should I start using pencil marks?

Start using pencil marks as soon as you move to medium puzzles. Medium puzzles regularly require candidate notation to spot naked pairs, hidden pairs, and pointing pairs. Without pencil marks, you will miss these patterns and get stuck. See our pencil marks guide for a complete introduction.

What is the difference between a naked pair and a hidden pair?

A naked pair is two cells in the same unit (row, column, or box) that share exactly the same two candidates and nothing else—the pair is “naked” because it is immediately visible. A hidden pair is two candidates that appear in only two cells within a unit, but those cells may also contain other candidates—the pair is “hidden” among the extras. Both techniques let you eliminate candidates: a naked pair removes those candidates from other cells in the unit, while a hidden pair removes the other candidates from the pair cells themselves. Learn more at naked pair and hidden pair.

Why do I get stuck on medium puzzles when I can solve easy ones?

Easy puzzles only require naked singles and hidden singles—you can solve them by scanning and placing numbers directly. Medium puzzles require candidate-based techniques like naked pairs, hidden pairs, and pointing pairs. The key difference is that you need pencil marks. Start by learning just one new technique at a time, and use that technique deliberately until it becomes natural.

Is NYT medium sudoku harder than SudokuPulse medium?

They are roughly comparable. Both platforms use the same intermediate techniques—naked pairs, hidden pairs, and pointing pairs. Individual puzzles vary in difficulty, but overall the difficulty bands are similar across NYT, sudoku.com, and SudokuPulse. If you can solve medium puzzles on one platform, you can solve them on any other.