Sudoku asks you to place the digits 1 to 9 on a 9×9 grid so that none repeats in any row, column or 3×3 box. Below, the methods are laid out in the order you'll actually need them, from a complete beginner's first move to the patterns that decide expert grids. The fastest way to absorb them is with a board in front of you — start on the easy puzzles and work up.
Pick a digit and follow it around the board. Find a box that doesn't have it yet, then trace the rows and columns crossing that box which already contain it. Wherever those lines rule out cells, what remains may be a single square: and that square is decided. Easy puzzles are built to fall to scanning alone, and even in evil grids scanning is what you keep coming back to between the fancy moves.
A useful discipline is to scan digits in order, 1 through 9, rather than wandering. It is slower for the first minute and much faster overall, because you stop re-checking the same digit and forgetting others entirely.
When scanning stops producing placements, write down what each empty cell could still be. Beginners should feel free to note every empty cell; the writing itself teaches you the board. From then on, the single most important habit is erasing: every time you confirm a digit, remove it from the notes of that row, that column and that box, in that fixed order. Most dead ends in intermediate sudoku are a missed erasure, not a missing technique.
Inside one box, if a digit's candidates are confined to a single row, that digit must appear in that row inside this box, so it can be erased from the rest of that row in the neighbouring boxes. The same works with columns, and in the other direction: if a digit in a row is confined to one box, it can be erased from the rest of that box. Nothing is placed, but the board gets simpler, and simpler boards produce placements.
Two cells in one unit holding exactly the same two candidates — say 3 and 7 — reserve both digits, so 3 and 7 leave every other cell of that unit. That is a naked pair. Turn it around: if two digits can only go into two cells of a unit, those cells belong to them and all their other candidates are erased — a hidden pair. Both extend to triples, three cells and three digits, which show up in the endgame of hard grids.
X-Wing: when a digit has exactly two possible cells in each of two rows and those cells share the same two columns, the digit can be erased from the rest of both columns. Swordfish is the same idea over three rows and three columns. Y-Wing works differently: three two-candidate cells linked as AB, BC and AC let you erase C from any cell that both wings can see.
The practical trick for finding them is to stop looking at the whole board and follow one digit at a time — nine sparse single-digit boards instead of one crowded grid. Rectangles and chains surface on their own once the noise is gone.
Every puzzle on this site has exactly one solution and can be reached by logic alone, so guessing is never necessary. It is also counter-productive: a grid you guessed your way through teaches you nothing, and a wrong guess usually reveals itself only twenty moves later, when the damage is untraceable. When you stall, assume there is a deduction you haven't found — and go back and find it. If you truly need to verify your work, the sudoku solver will tell you whether your board is still consistent.
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