Sudoku Solving Strategies — Complete Overview
One of the most frustrating moments in sudoku is being stuck without knowing what to try next. This guide presents all core solving strategies in order of complexity — from the simplest techniques that solve every easy puzzle to the advanced methods needed for expert grids. Use it as a reference whenever you need to know what to try.
Level 1: Beginner Strategies
Last Remaining Cell
The simplest pattern: a row, column, or box has exactly one empty cell. The missing digit (the one not yet in that group) is the answer. No elimination needed — just count what's present.
Naked Single
An empty cell has only one possible digit after checking its row, column, and box. All other eight digits are already present in the combined constraints. Fill it in. See: Naked Singles →
Digit Scanning (Cross-Hatching)
Pick a digit. For each incomplete box, use existing instances of that digit in rows and columns to eliminate cells inside the box. If only one cell remains, place the digit. See: Scanning Method →
Level 2: Intermediate Strategies
Hidden Single
A digit can only go in one cell within a row, column, or box — even though that cell appears to have multiple candidates. The uniqueness is "hidden" because you discover it by examining the group, not the cell. See: Hidden Singles →
Naked Pair
Two cells in the same group each contain exactly the same two candidates. Those two digits can be eliminated from all other cells in that group. See: Naked Pairs →
Naked Triple
Three cells in the same group collectively contain only three distinct candidates (across all three cells). Eliminate all three digits from the rest of the group.
Hidden Pair
Two digits can only appear in the same two cells within a group. Even if those cells have other candidates, the two digits are "locked" in those cells. Eliminate all other candidates from those two cells.
Level 3: Advanced Strategies
Pointing Pair / Pointing Triple
All candidates for a digit within a box are confined to one row or column. Eliminate that digit from the rest of that row or column outside the box. See: Pointing Pairs →
Box-Line Reduction
All candidates for a digit within a row or column are confined to one box. Eliminate that digit from other cells in that box. See: Box-Line Reduction →
X-Wing
A digit appears as a candidate in exactly two cells in each of two rows, and those cells align in the same two columns. The digit must be in one of two diagonal pairs. Eliminate the digit from all other cells in those two columns.
Swordfish
An extension of X-Wing using three rows and three columns. The digit appears in at most three cells per row, all within the same three columns. Eliminate the digit from all other cells in those three columns.
How to Use This Reference
When you're stuck, work through the levels in order:
- Exhaust all naked singles and hidden singles first — they're fast and often overlooked.
- Check for naked and hidden pairs in every group with pencil marks set up.
- Scan for pointing pairs and box-line reductions across all boxes, rows, and columns.
- Only try X-Wing and Swordfish after the above methods are exhausted.
The most common mistake is jumping to complex strategies while simpler ones are still available. Always exhaust the current level before moving up.
Difficulty Level Guide
| Difficulty | Strategies Required |
|---|---|
| Easy | Naked singles, last remaining cell, basic scanning |
| Medium | + Hidden singles |
| Hard | + Naked pairs, pointing pairs, box-line reduction |
| Expert | + Hidden pairs, naked triples |
| Evil | + X-Wing, Swordfish, and beyond |