Evan TessellA classic Sudoku has nine rows, nine columns, and nine outlined boxes. Every row, column, and box must contain the digits 1 through 9 once each. The printed digits are clues. Keep them in place and fill only the empty cells. Nikoli's rules provide the compact version of this structure.
Begin with a nearly complete row rather than the first empty square you happen to see. Suppose a row contains 1, 2, 3, 4, 5, 6, 8, and 9. Its remaining cell must be 7. Before writing, look down that cell's column and around its box. In a correctly copied puzzle, the 7 should fit all three units.
If a row has two blanks, list both missing digits. Then inspect one blank's column and box. A visible copy of one missing digit rules it out at that location. You have turned a broad search into a small, checkable question.
Write a final digit only when you can explain why it belongs. A useful sentence is, "This row needs 4 and 6; the column already has 4, so this cell is 6." The sentence matters more than speed.
After each placement, revisit the same row, column, and box. A single new digit may resolve a neighboring blank. If nothing follows, move to another nearly complete unit. You do not need to work in reading order or finish a whole region before exploring somewhere else.