Sudoku techniques: how to solve each one

Every technique the game uses to grade puzzles and to explain its hints, from the first moves any solver learns to the chains that only the hardest puzzles need. Each guide explains the idea in plain words and walks through a step from a real puzzle.

The basics

  • Naked single — A naked single is a cell where only one digit can still go, because the other eight already appear in its row, column or box.
  • Hidden single — A hidden single is a digit that has only one possible place left in a row, column or box, even if that cell still has other candidates.

Needed from Medium

  • Locked candidates — Locked candidates remove a digit from a row, column or box when all of its remaining spots in another unit line up.

Needed from Hard

  • Naked pair — A naked pair is two cells in a unit that hold the same two candidates, which lets you remove those digits from the rest of the unit.
  • Hidden pair — A hidden pair is two digits that can only go in the same two cells of a unit, so those cells can hold nothing else.

Needed from Very Hard

  • Naked triple — A naked triple is three cells in a unit that between them hold only three candidates, which can be removed from the rest of the unit.
  • X-Wing — An X-Wing is a digit that has exactly two spots in each of two rows, in the same two columns, which clears it from the rest of those columns.
  • Empty rectangle — An empty rectangle uses a digit confined to one row and one column of a box, plus a two-place link elsewhere, to remove the digit from one cell.

Needed from Expert

  • Hidden triple — A hidden triple is three digits that can only go in the same three cells of a unit, so those cells can hold nothing else.
  • Naked quad — A naked quad is four cells in a unit that between them hold only four candidates, which can be removed from the rest of the unit.
  • XY-Wing — An XY-Wing is a pivot cell with two candidates and two wing cells, which together force a digit out of the cells the wings both see.
  • XYZ-Wing — An XYZ-Wing is a three-candidate pivot with two wings, which removes a digit from cells that see all three cells.
  • Finned X-Wing — A finned X-Wing is an X-Wing with an extra candidate (a fin) in one box, which still clears the digit from that box.
  • Swordfish — A Swordfish is a digit confined to the same three columns across three rows, which clears it from the rest of those columns.
  • WXYZ-Wing — A WXYZ-Wing is four cells holding four digits between them, where one digit must land in at least one of them, clearing it from cells that see them all.
  • Simple coloring — Simple coloring follows a chain of two-place links for one digit, colors the cells in two colors, and uses the colors to remove candidates.
  • Unique rectangle — A unique rectangle uses the rule that a puzzle has one solution to rule out a pattern of four cells that could be swapped.
  • W-Wing — A W-Wing is two cells with the same two candidates, joined by a strong link on one of the digits, which clears the other digit from cells that see both.
  • Finned Swordfish — A finned Swordfish is a Swordfish with an extra candidate (a fin) in one box, which still clears the digit from that box.
  • X-chain — An X-chain links two-place spots for one digit end to end, and removes the digit from cells that see both ends.
  • XY-chain — An XY-chain is a sequence of two-candidate cells, each sharing a digit with the next, that removes a digit from cells that see both ends.
  • Hidden quad — A hidden quad is four digits that can only go in the same four cells of a unit, so those cells can hold nothing else.
  • Jellyfish — A Jellyfish is a digit confined to the same four columns across four rows, which clears it from the rest of those columns.

New to the game? Start with how to play, or play a puzzle and ask for hints: each hint names the technique it uses and explains why it works.