Sudoku Tutorial Step 4:The Single Candidate Rule: Filling the Obvious Numbers

Welcome back to Sudoku Fun! In Article 3 you learned how to systematically scan the grid. Now it's time to learn the single most important technique in beginner sudoku: the Single Candidate Rule, also called the Naked Single. This technique alone can solve the majority of Easy-level puzzles.

Practice Naked Singles — Try This Puzzle!

How to play:
Fill empty cells with numbers 1–9. Each row, column, and 3×3 box must contain all digits 1–9.
Red = duplicate. Green = your answer. Gray = given clue.

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# The Single Candidate Rule: Filling the Obvious Numbers

Quick Summary: The Single Candidate Rule — also called the Naked Single — is the simplest and most powerful technique in beginner sudoku. When a single empty cell has only one possible number that can legally go there (after checking its row, column, and 3×3 box), that number must be the correct one. This is not guessing — it is pure logical certainty, grounded in a fundamental principle of logic called the Law of the Excluded Middle.

🧠 The Logic Behind It — The Law of the Excluded Middle: In classical logic, the Law of the Excluded Middle states that for any proposition, either that proposition is true or its negation is true — there is no third option. Applied to sudoku: for any empty cell, the correct number is one of the digits 1–9. If you can logically exclude eight of those nine digits (because they already appear in the same row, column, or box), then the remaining one must be correct. There is no alternative. This is the logical engine behind every Naked Single you will ever find.

# What Exactly Is a "Naked Single"?

A Naked Single is a cell where, after checking all constraints, only one number from 1 to 9 is not eliminated. The term "naked" means it is obvious — the cell's unique candidate is visible to anyone who systematically checks.

Here is the step-by-step process for finding a Naked Single:

Step 1 — Pick an empty cell. Look at the cell you want to fill.

Step 2 — Check the row. Look across the entire row that contains this cell. Every number already present in this row is eliminated as a candidate for this cell.

Step 3 — Check the column. Look down the entire column. Every number already present in this column is also eliminated.

Step 4 — Check the 3×3 box. Look at all nine cells in the 3×3 box containing this cell. Every number already present in this box is eliminated.

Step 5 — Count remaining candidates. After eliminating all numbers that appear in the cell's row, column, or box, how many numbers from 1–9 remain possible? If the answer is exactly one, you have found a Naked Single. That number is guaranteed to be correct.

▲ A Naked Single: start with 9 possible digits, eliminate everything that conflicts with the row, column, and box. If exactly 1 remains — you have your answer.

# A Real-Life Analogy: The Detective's Method

Imagine a detective investigating a crime with exactly nine suspects. Through evidence, the detective eliminates suspects one by one:

— Three suspects have alibis confirmed by witnesses (these are like numbers blocked by the row).

— Four more are ruled out by forensic evidence (these are like numbers blocked by the column).

— One more is ruled out by surveillance footage (this is like a number blocked by the box).

Only one suspect remains. The detective does not "guess" that this person is guilty — all other possibilities have been logically eliminated. This is exactly how the Naked Single technique works. As Sherlock Holmes famously said: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth."

💡 Why "Naked"? The term "naked" refers to the fact that this single candidate is plainly visible once you check the cell's row, column, and box. There is no subtle pattern to discover — it is a straightforward "what numbers are still possible here?" check. This distinguishes it from Hidden Singles (our next tutorial), which require a different angle of observation.

# Finding Naked Singles Faster: Practical Tips

You can methodically check every empty cell for Naked Singles, but that is slow. Experienced solvers use these shortcuts to find them faster:

🔹 Tip 1: Start with the most constrained cells. A cell sitting in a row, column, and box that together already contain many different numbers is your best place to look. The more numbers already "surrounding" a cell, the fewer candidates remain — and the more likely exactly one candidate is left. Think: "This row already has 6 distinct numbers, this column adds 2 new ones, and this box adds 1 more — that's 8 numbers blocked. The 9th must go here!"

🔹 Tip 2: Use your scanning pass to trigger Naked Single discovery. During your full scan (Article 3), when you check off numbers in a row/column/box, you are simultaneously building the elimination list for every empty cell in that row/column/box. After each scan pass, ask: "Which cells now only have one candidate left because of what I just placed?"

🔹 Tip 3: Look at cells near the edges of filled areas. If a 3×3 box has 6 filled cells, the remaining 3 empty cells are heavily constrained. Check them first — at least one is often a Naked Single.

▲ Prioritize cells in nearly-complete rows, columns, and boxes — these are where Naked Singles appear most frequently.

# Common Mistakes When Using Naked Singles

🔴 Mistake 1: Checking only the box or only the row. A Naked Single requires checking all three constraints (row, column, AND box). Many beginners check only the box and miss that the column already contains the number they are about to place. Fix: Always do the triple-check — row, column, box — in that order, every time.

🔴 Mistake 2: Miscounting eliminated numbers. If eight numbers are eliminated and only one remains, that one is correct. But if you miscount and think eight are eliminated when only seven actually are, you might place a number that has a valid alternative — a mistake. Fix: Use your fingers to count eliminated numbers, or use pencil marks (write tiny numbers 1-9 in the corner of the cell and cross them out as you eliminate).

⚠️ The Pencil Mark Shortcut: For a heavily constrained cell, instead of mentally tracking all eliminations, write the digits 1–9 small in the corner of the cell. Cross out each one as you check row, column, and box. If exactly one remains uncrossed, that is your Naked Single. This is the foundation of candidate notation, which we will cover in depth in an upcoming tutorial.

🔴 Mistake 3: Trusting your memory over re-checking. "I think I already checked this column..." — no. Check it again. Every time. Your working memory is more fallible than you think, especially as the puzzle gets more filled-in and the cognitive load increases. Fix: When in doubt, re-scan the row, column, and box. It takes 10 seconds and prevents 10 minutes of frustration.

# Naked Single vs. Hidden Single — Know the Difference

This is a concept that trips up many beginners. Let's clarify it now:

Naked Single (this tutorial): You focus on one cell. In that cell, only one number is possible because all other eight numbers are blocked by the row, column, or box. You think: "What can this cell be?"

Hidden Single (next tutorial): You focus on one number. In a given row, column, or box, that number can only go in one specific cell — even though the cell itself might have multiple candidates. You think: "Where can this number go?"

▲ Naked Single: one cell, one candidate. Hidden Single: one number, one possible cell. They are the same logic viewed from opposite directions.

# Practice: Find the Naked Singles

Open the interactive puzzle at the top of this page. Before you solve it, try this exercise:

1. Do one complete 1→9 full scan.

2. After the scan, look at the 3×3 box in the top-left corner of the puzzle. How many cells there have only one possible candidate after checking their row, column, and box?

3. Fill in every Naked Single you can find across the entire grid.

4. Do another 1→9 scan — new Naked Singles should have appeared!

5. Repeat until the puzzle is solved.

This alternating rhythm — scan → find naked singles → scan → find more naked singles — is the core solving loop for all Easy and most Medium sudoku puzzles. Master this rhythm and you can confidently solve any Easy puzzle.

# Frequently Asked Questions

Q: What is the difference between a Naked Single and just "guessing"?
A: Guessing means picking a number without certainty. A Naked Single is not a guess — it is a logically necessary conclusion. When eight of nine numbers are proven impossible by direct observation, the ninth is guaranteed to be correct. This is deduction, not guesswork.

Q: How many Naked Singles are usually in an Easy puzzle?
A: In a typical Easy puzzle (with ~35-40 given clues), roughly 60-70% of the empty cells can be solved using Naked Singles alone. The remaining cells usually require Hidden Singles or basic elimination — which we will cover next.

Q: What if I check a cell and find zero possible numbers?
A: This means a mistake was made earlier — you placed a number that contradicts the puzzle's solution somewhere. Use the Undo button to backtrack and find the error. A valid sudoku always has at least one legal candidate for every empty cell.

Q: Can I use pencil marks instead of mentally checking each cell?
A: Yes, and for harder puzzles you absolutely should. Write tiny numbers 1-9 in each empty cell, then cross out the ones eliminated by row/column/box. When only one remains, erase all the crossed-out numbers and fill in that digit. We will cover pencil mark technique in depth in an upcoming tutorial.

# Key Takeaways

📝 Summary — 3 Things to Remember:
🔹 A Naked Single is logical certainty, not a guess. When exactly one number from 1–9 is not eliminated by the cell's row, column, or box, that number is guaranteed correct. This is the Law of the Excluded Middle in action.
🔹 Scan first, then hunt for Naked Singles. Your scanning pass (Article 3) naturally sets up the conditions for finding Naked Singles. After each scan, check the most constrained cells for single candidates.
🔹 Always triple-check: row + column + box. A cell belongs to all three constraint zones. Missing even one zone can lead to placing a number that appears to be a Naked Single but actually is not. Three checks, every time, no exceptions.

# Next Step

Now you have two powerful techniques: scanning and observation (Article 3) and the Single Candidate Rule / Naked Single (this article). With these two tools alone, you can solve most Easy puzzles. But there is another kind of "single" — the Hidden Single — which approaches the same logic from the opposite direction. Instead of asking "what can this cell be?", you ask "where can this number go?"

👉 Next: Hidden Singles: Finding Numbers That Only Have One Place to Go

How many Naked Singles did you find in the puzzle above? Share your solving time in the comments — we bet you're faster than last time! ⏱️🧠

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