Sudoku tips

Solving tips

How to solve Sudoku

Every Sudoku can be solved by logic, without guessing. The trick is to use the right technique at the right time: quick scanning for the easy cells, notes and pattern-spotting for the hard ones. This is the short version, in the order you will need them. Each technique has its own page with a worked example.

Read the Rules

Where Sudoku came from

The puzzle began as Number Place in an American magazine in 1979, got the name Sudoku in Japan in the 1980s, and went around the world from 2004, when newspapers began printing it daily.

Orion in a graphite jacket works on a paper Sudoku at a table.
Sudoku spent its first years as a magazine puzzle before it went worldwide.

Scan for singles first

Start without notes. Take one digit at a time and see where the copies already on the board leave room for another. A digit with one possible cell in a box, row or column is a hidden single. A cell with one possible digit is a naked single. Easy puzzles need nothing else.

“Before anything clever, finish the obvious. Most grids give up more than you expect.”

Orion
Hidden single
Naked single
Left: the other 7s leave one home for 7 in the box. Right: the shaded digits leave only 5 for the square.

Write notes and look for pairs

When the singles run out, write each cell’s candidates as notes and look for small groups. Two cells that share the same two candidates, or two digits that share the same two cells, let you clear notes around them.

Before
After
The two shaded squares hold 2 and 6 in some order, so the last square must be 8.

Pointing and box-line reduction

Where a box and a line overlap, a digit confined to the overlap can be cleared from the rest of the line or the rest of the box.

This is the step solvers miss most often. When a medium puzzle stalls, check each box for it.

In this box the 4 can only sit in row 2, so no other square in that row can be 4.

The X-Wing

On hard grids, one digit can be tied to the four corners of a rectangle, across two rows and two columns. Finding the rectangle clears that digit from the rest of both columns.

The 3s must take opposite corners of the rectangle, so they use up both columns.

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.
Orion points to an open puzzle notebook with a blue pencil.
One elimination often opens several singles. Go back and scan.