How to solve Sudoku

01 · Sudoku

Where Sudoku came from

The puzzle was first published in 1979 in an American puzzle magazine under the name Number Place. A Japanese publisher, Nikoli, brought it to Japan in the 1980s and gave it the name Sudoku, short for a phrase meaning that each digit must appear only once. It became a worldwide craze in 2004 and 2005, when British and then American newspapers began printing it daily.

02 · Sudoku

Scan for singles first

Take each digit from 1 to 9 in turn and see where it already sits. Each copy rules out its row, column and box. When only one cell in a box, row or column can still take the digit, that is a hidden single: place it.

A naked single is the other way round: a cell where its row, column and box together already contain eight different digits, leaving one. Easy puzzles fall to singles alone.

03 · Sudoku

Write notes and look for pairs

When the singles run out, fill in candidates as notes. Then look for groups. If two cells in a unit hold only the same two candidates, they form a naked pair, and those digits can be removed from the rest of the unit. Three cells sharing three candidates work the same way.

Hidden pairs are the mirror image: two digits that can only go in the same two cells of a unit. Those cells must hold those digits, so any other candidates in them can be erased.

04 · Sudoku

Pointing and box-line reduction

If, inside one box, every possible place for a digit lies in the same row, then the digit must be in that row within that box. You can remove it from the rest of that row outside the box. This is called a pointing pair or triple.

The reverse also works: if in one row all the places for a digit lie inside one box, remove the digit from the other cells of that box.

Pointing is the technique most solvers learn last and miss most often. When a medium puzzle stalls, check each box for it.

05 · Sudoku

The X-Wing

For hard grids, look for a digit that has exactly two possible cells in each of two rows, and those cells sit in the same two columns. The digit must occupy one diagonal of that rectangle or the other, so it can be removed from every other cell in those two columns. The same pattern works with rows and columns swapped.

06 · Sudoku

Solving habits that save time

• Go back to scanning after every hard deduction; one elimination often opens several singles.
• Keep notes current. Clear candidates as soon as you place a digit.
• If the board reports a conflict, undo back to your last certain move rather than patching around it.