Good sudoku solving is not trial and error — it is a sequence of logical patterns called techniques. Below are five techniques ordered from easiest to hardest. NUMBACK's AI coach classifies every move you make into these techniques and tells you which ones slow you down.
A cell where only one candidate remains. Cross off every digit already present in that cell's row, column and box, and if exactly one digit survives, it goes there. It is the most basic technique and also the most commonly missed one. After placing any digit, rescan the row, column and box you just changed.
The cell itself may still have several candidates, but within a row, column or box there is only one cell where a particular digit can go. Sweep digits 1 through 9 systematically through rows, then columns, then boxes, and hidden singles fall out mechanically.
If, inside one box, a digit can only go in cells that all share a single row or column, then that digit can be eliminated from the rest of that row or column outside the box — this is pointing. The mirror case, where a digit within a row is confined to a single box, lets you eliminate it from the rest of that box — claiming. These moves do not place a digit directly; they thin out candidates so the next single appears.
When two cells in the same unit hold exactly the same two candidates — say both are {3,7} — those two digits must occupy those two cells, so 3 and 7 can be removed from every other cell in that unit. The same logic extends to triples across three cells. Pencil-marking only the two-candidate cells makes pairs jump out.
For a given digit, find two rows where that digit can only appear in the same two columns. The digit can then be eliminated from those two columns in every other row. The pattern works identically with rows and columns swapped. It is the gateway to advanced solving and is often what breaks a hard puzzle open when basic techniques stall.