The best way to learn Sudoku is to watch a puzzle being solved while understanding the reasoning behind every move. In this walkthrough, we solve a medium-difficulty puzzle from start to finish, calling out each strategy as we apply it.
Every solve begins with an initial scan of the grid. The goal is to identify the low-hanging fruit: cells or regions where the answer is immediately obvious. Look for nearly complete rows, columns, or boxes, frequently appearing numbers, and intersections of populated regions where naked singles may appear.
After the opening scan, the next phase uses hidden singles found through cross-hatching. This technique picks a specific number and checks each box to find where that number can go. By drawing imaginary lines along rows and columns where the number already appears, you eliminate cells within each box until only one possibility remains.
After exhausting all obvious singles, we transition to pencil marking. For each empty cell, we write down every number that is still a valid candidate based on the row, column, and box constraints. Work by region, skip obvious cells that resolve immediately, stay accurate, and update after every placement.
With pencil marks in place, we can now see patterns that were invisible before. Intermediate techniques include naked pairs, pointing pairs, and hidden pairs. Each technique creates a chain reaction where eliminations lead to new placements, which update pencil marks elsewhere and reveal more patterns.
After the intermediate techniques, our puzzle has significantly fewer empty cells. At this point, we return to basic scanning because the grid is now populated enough for simpler methods to work again. The final cells typically fall into place rapidly through basic logic alone.
Phases 1-2 used naked singles and hidden singles via cross-hatching to place 13 numbers. Phase 3 set up pencil marks and found 3 additional naked singles. Phase 4 applied naked pair, pointing pair, and hidden pair for 16 more placements. Phase 5 resolved the final 12 cells through a cascade of singles.
Always start with the simplest techniques before moving to complex ones. Pencil marks are a tool, not a crutch. Each placement creates opportunities elsewhere in the grid. Alternate between basic scanning and advanced techniques as the grid evolves. Every properly constructed Sudoku can be solved without guessing.
Start by scanning for naked singles (cells with only one possible number), then look for hidden singles (numbers that can only go in one cell within a row, column, or box). Use pencil marks to track candidates, then apply elimination techniques like naked pairs and pointing pairs. Work systematically through the grid, always filling in the most certain placements first.
Begin with a full grid scan looking for rows, columns, or boxes that are nearly complete (missing only one or two numbers). These give you the easiest initial placements. Then use cross-hatching: pick a number and scan each box to see where it can go by checking intersecting rows and columns.
Pencil marks are small candidate numbers written in cells to track which values are still possible. Use them when simple scanning no longer reveals obvious placements, typically after filling in all naked and hidden singles. Pencil marks make patterns like naked pairs and X-Wings visible.
Work from simplest to most complex. First check for naked singles, then hidden singles, then naked pairs, then hidden pairs, then pointing pairs and box-line reduction. Only move to advanced techniques like X-Wing or Swordfish when simpler methods stop producing results. Most puzzles up to medium difficulty can be solved with singles and pairs alone.
An easy puzzle solved step by step typically takes 5 to 15 minutes for an intermediate player. Medium puzzles take 15 to 30 minutes. Hard puzzles can take 30 minutes to over an hour. The time depends on your familiarity with techniques and how quickly you can scan the grid.
Yes, every properly constructed Sudoku puzzle with a unique solution can be solved purely through logic without any guessing. If you feel the need to guess, it means there is a technique you have not yet applied. Learning more advanced strategies eliminates the need for trial and error.
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