Sudoku: Solving Techniques for Beginners

The One Rule That Solves Half The Board

Sudoku's only rule is: each row, each column, and each 3x3 box must contain the digits 1 through 9 exactly once. Every solving technique is just a clever way of applying that rule. Internalize this — when you are stuck, ask "what number is forbidden in this cell because of the rule?" and you will often find the answer.

Technique 1: Scanning (Cross-Hatching)

Scanning is what you should do at the very start of every puzzle. Pick a digit (say, 5) and scan the board for existing 5s. Each 5 forbids other 5s in its row, its column, and its box. After scanning all the existing 5s, look at each 3x3 box that does *not* contain a 5 — within that box, the forbidden cells form a pattern, and if only one cell in the box is left un-forbidden, that cell must be the 5.

Repeat this for every digit from 1 to 9. Easy puzzles can be fully solved by scanning alone.

Technique 2: Naked Singles

A naked single is a cell where eight of the nine digits are already forbidden (by row, column, and box), leaving only one possible value. To find naked singles, look at empty cells one at a time and mentally list what digits are still legal. If only one digit is legal, write it in.

This sounds tedious but it is the workhorse of intermediate puzzles. With practice you can scan a cell in under two seconds.

Technique 3: Hidden Singles

A hidden single is the inverse of a naked single: instead of looking at a cell and asking "what can go here?", you look at a row, column, or box and ask "where can the digit 5 go in this row?". If only one cell in the row can hold a 5, that cell holds the 5 — even if that cell had other legal candidates.

Hidden singles are easy to miss because they require looking at units (rows/cols/boxes) rather than individual cells. Make a habit of, after every entry, scanning the affected row, column, and box for hidden singles.

Technique 4: Naked Pairs

Sometimes two cells in the same row, column, or box have *exactly the same two candidates* — say, both cells can only be 3 or 7. Even though you do not know which is which, you know one is 3 and the other is 7. That means no other cell in that row, column, or box can be 3 or 7. Cross those candidates off the other cells.

Naked pairs are the first technique that feels like real deduction rather than just elimination. They appear in every medium-difficulty puzzle and many easy ones.

Technique 5: The Box-Line Reduction

If a digit's only candidates within a 3x3 box all happen to lie on the same row (or same column), then that digit must appear in one of those cells — and therefore cannot appear anywhere else in that row (or column), even outside the box. Cross those candidates off.

This is a specific case of "intersection" logic, but it accounts for a surprisingly large fraction of puzzle-breaking moves. Train your eye to spot boxes where a single digit's candidates line up.

What About Guessing?

You should not guess. Ever. A well-formed Sudoku has exactly one solution and that solution is reachable by pure logic. If you find yourself wanting to guess, it means you missed a technique — go back and re-scan for hidden singles, naked pairs, and box-line reductions. Guessing leads to "well what if I'm wrong" chains that waste time and erode your logic muscle.

A Practice Workflow

1. Scan each digit 1-9 once at the start. 2. After each entry, scan the affected row, column, and box for naked singles and hidden singles. 3. When singles run dry, look for naked pairs. 4. When naked pairs run dry, look for box-line reductions. 5. Only after all four techniques are exhausted should you reach for advanced methods (X-Wing, swordfish, coloring).

This workflow solves roughly 90% of newspaper-difficulty puzzles. The remaining 10% need advanced techniques, but you should not worry about those until you can solve the easy 90% in under ten minutes.

Summary

• Scanning solves easy puzzles; do it first every time.
• Naked singles are the workhorse — practice finding them fast.
• Hidden singles hide in plain sight; scan units, not just cells.
• Naked pairs let you cross off candidates from other cells.
• Box-line reduction catches what singles miss.
• Never guess. If you are stuck, you missed a technique.

Sudoku rewards patience more than IQ. A methodical beginner who applies these five techniques will out-solve a clever player who skips steps, every time.