Naked Single - The Most Fundamental Solving Technique in Sudoku

A Naked Single refers to a situation where only one possible digit remains for a specific cell. Every digit already placed in the row, column, and block that the cell belongs to is removed from its candidate list, so if the eliminations leave exactly one digit standing, that digit is confirmed. Let us walk through a concrete example. Suppose that for a given cell, the same row already contains 1, 2, 3, 4 and 5, the same column contains 7 and 8, and the same block contains 9. Eight of the digits from 1 to 9 are therefore impossible, and only 6 remains, so the cell is confirmed as 6. The important point here is to gather your eliminations from all three directions. If you glance only at the row, conclude that "two candidates are still left" and move on, you will miss the final elimination that the column or the block would have handed you, and with it the confirmation sitting right in front of you.

The most reliable way to find Naked Singles is to write out the candidates using the pencil-mark feature. Once they are written out, any cell with a single candidate is visible at a glance, but maintaining marks across all 81 cells is laborious, and every confirmation forces you to rewrite them. In practice, then, the effective compromise is not to mark the whole grid but to write out candidates locally, only in the region where you feel stuck. The places worth targeting are cells whose row, column and block are all well filled in, the intersections where constraints pile up. The denser the surroundings, the more digits you can eliminate, and the more easily the candidate list drops to one. Conversely, no amount of staring at a cell surrounded by empty space will narrow anything down; only your time will run out. Treat pencil marks not as a tool for writing everything down but as a tool for verifying the places most likely to narrow, and you gain both speed and certainty.

Easy-level puzzles are built so that a chain of Naked Singles alone can carry you to the finish. Confirming one cell turns that digit into a fresh elimination condition, which reduces another cell that shares its row, column or block to a single candidate. Because this ripple spreads across the whole grid, the puzzle fills in completely without ever calling on another technique. What people most often misunderstand here is the idea that difficulty can be measured by the number of clues. A grid with many clues is not necessarily easier, and one with few clues is not necessarily harder. What determines difficulty is which techniques you are forced to use in order to finish. Grids that need nothing beyond Naked Singles sit at the easy end, and grids where you cannot avoid Hidden Singles or Naked Pairs sit above them. Treating clue count and difficulty as separate matters is the correct view from both the setter's and the solver's side.

At Medium difficulty and above, you will inevitably reach a point where Naked Singles alone no longer move you forward. Every cell still holds two or more candidates, and no amount of further elimination brings one down to a single digit. This does not mean the grid is wrong; it means the information available from the "look at the cell" direction has simply run out. When you feel you have hit that wall, switching viewpoints is faster than circling the grid again and again with the same search. The next techniques, such as Hidden Singles and Naked Pairs, are all tools that shave candidates from a different angle than Naked Singles, and the eliminations they yield give birth to new Naked Singles in turn. Knowing the limit accurately also keeps you from mistaking a genuine dead end for your own oversight and burning time over it.

Once you have a sense of where to look, the next thing to settle is the order in which you scan. A good default is to sweep the nine blocks in a fixed order from top-left to bottom-right, checking the empty cells one at a time within each block. Fixing the order means you no longer have to remember how far you got, which cuts both the waste of examining the same place twice and the gaps left by skipping a place entirely. The other habit that pays off is the local scan immediately after a confirmation. When you fill in a digit, review only the empty cells that share its row, column or block before returning to the full sweep. The candidates that changed are confined to that range, so if a new Naked Single has appeared, that is where it will be. Use the full sweep to gather candidate locations broadly, and the local scan after each confirmation to collect the chain. This two-tier approach is what separates you from someone drifting aimlessly across the grid.

The value of a Naked Single lies less in filling one cell than in the chain it sets off. When you confirm a digit in a cell, that digit disappears at once from the candidates of every cell sharing its row, column or block. As many as 20 cells are affected, and if any one of them drops to a single candidate, the next Naked Single is born. The chain does not run in a straight line but branches, so it is not unusual to confirm two or three cells in succession after a single confirmation. Conversely, if you neglect the review that follows a confirmation, a Naked Single that should have surfaced is left stranded on the grid, and later you feel as though you are stuck. That feeling of being stuck is usually not the difficulty of the puzzle but a dropped link in the chain. Make "fill it in, then review the surroundings" a single motion you perform without thinking.