Solving Techniques
Easy
Hidden Single
Also known as: Last Remaining Cell, Pinned Digit.
Summary: In a row/column/box (or any house) you can only put digit X in only one of the cells, so put it there.
Detailed explanations: sudoku.com, sudokuwiki.org, sudopedia.org, HoDoKu.
Naked Single
Also known as: Obvious Single, The Last Possible Number, Forced Digit, Sole Candidate.
Summary: A cell has only one possible digit, so write it in.
Detailed explanations: sudoku.com, sudopedia.org, sudokuwiki.org, HoDoKu.
Thermo Single
Summary: Only applies to Thermo puzzles.
For a thermometer, starting from the bulb and going to the ending cell, find the smallest digit that can be a candidate in each cell.
Do the same thing starting at the end and going towards the bulb and find the highest digits.
If you find a cell where the lowest digit is also the highest you can fill it in.
Practice puzzle: 1.
Palindrome Values
Summary: Only applies to Palindrome puzzles.
Whenever we fill in a digit on a palindrome we can automatically fill it in on the other side of the palindrome.
Medium
Candidates
Also known as: Pencil marks, Notes.
Summary: Write all the possible values in each cell.
Detailed explanations: sudoku.com.
Hidden Pairs
Also known as: Last 2 Remaining Cells.
Summary: In a row/column/box (or any house) you can only put digits X and Y in two of the cells, so remove every other candidate from those two cells.
Detailed explanations: sudoku.com, sudopedia.org, sudokuwiki.org, HoDoKu.
Naked Pairs
Also known as: Obvious Pairs.
Summary: In a row/column/box (or any house) two cells can only contain digits X and Y, so you can remove them as candidates from every other cell in the same house.
Detailed explanations: sudoku.com, sudopedia.org, sudokuwiki.org, HoDoKu.
Locked Candidate Pairs
Also known as: Intersection Removal, Line-Box Interaction, Pointing Pairs, Claiming/Box-Line Reduction.
Summary: In a row/column/box A, there are two candidate cells for digit X. If there is another row/column/box B that contains those two cells, remove X as a candidate from all other cells in B.
Example: In column 3, digit 3 must be in box 1. Therefore, 3 cannot be a candidate of any other cell in the same box.
Detailed explanations: sudoku.com, sudokuwiki.org, sudopedia.org, HoDoKu.
Thermo Candidates
Summary: Only applies to Thermo puzzles.
Same as Thermo Single, but we use it to remove candidates. You can remove any candidates from a cell that are not between the lowest and the highest valid candidate.
Example: The bulb cell has candidates 2,3. The next cell has candidates 2,3,5 and you can remove 2.
Practice puzzle: 1.
Palindrome Candidates
Summary: Only applies to Palindrome puzzles.
Whenever we update a palindrome cell's candidates we can automatically do the same on the other side of the palindrome.
Kropki Dot Pair Logic
Summary: Only applies to Kropki puzzles.
For a kropki dot, find all valid digit combinations in the corresponding pair of cells. Remove all candidate digits that do not appear in any combination.
Practice puzzle: 1.
Kropki Dot Chain Logic
Summary: Only applies to Kropki puzzles.
Same as Kropki Dot Pair Logic, but apply for a chain of cells linked by dots in the same house.
Practice puzzle: 1.
Kropki Dot Chain Advanced Logic
Summary: Only applies to Kropki puzzles. It is a variation of Kropki Dot Chain Logic where we look deeper into the consequences.
If one chain combination eliminates all candidates from a cell, remove the combination as a candidate.
Killer Cage Candidates
Also known as: Sum Elimination.
Summary: Only applies to Killer puzzles.
For a killer cage, find all digit combinations that satisfy the sum. Remove all candidate digits that do not appear in any combination.
Detailed explanations: killersudokuonline.com (Sum Elimination).
Practice puzzle: 1.
Killer Sum Rule
Also known as: Rule of 45.
Summary: Only applies to Killer puzzles.
The sum of digits in a 9 cell house is 1+2+...+9 = 45.
Starting with 45, you can subtract all of the cage sums that are fully within the same house and you get the sum of the rest of the cells. If there is only one cell left, you found the value of that cell.
For other house sizes use a different 1+2+...+n.
Detailed explanations: killersudokuonline.com (Rule of 45).
Practice puzzle: 1.
Arrow Candidates
Summary: Only applies to Arrow puzzles.
For an arrow, find all digit combinations that satisfy the sum. Remove all candidate digits that do not appear in any combination.
Arrow Advanced Candidates
Summary: Only applies to Arrow puzzles. It is a variation of Arrow Candidates where we look deeper into the consequences.
If one arrow combination eliminates all candidates from a cell, remove the combination as a candidate.
Renban Candidates
Summary: Only applies to Renban puzzles.
For a renban, find all digit combinations that are a unique consecutive set of digits. Remove all candidate digits that do not appear in any combination.
Top-Bottom Candidates
Summary: For each row X we track the cells with candidate X where the sequence 1 to X can arrive on. For the decreasing sequence on row X we track digit 10-X.
Hard
Hidden Triples
Also known as: Last 3 Remaining Cells.
Summary: In a row/column/box (or any house) you can only put digits X, Y and Z in three of the cells, so remove every other candidate from those three cells.
Detailed explanations: sudoku.com, sudopedia.org, sudokuwiki.org, HoDoKu.
Practice puzzle: 1.
Naked Triples
Also known as: Obvious Triples.
Summary: In a row/column/box (or any house) three cells can only contain digits X, Y and Z, so you can remove them as candidates from every other cell in the same house.
Detailed explanations: sudoku.com, sudopedia.org, sudokuwiki.org, HoDoKu.
Locked Candidate Triples
Also known as: Intersection Removal, Line-Box Interaction, Pointing Pairs, Claiming/Box-Line Reduction.
Summary: In a row/column/box A, there are three candidate cells for digit X. If there is another row/column/box B that contains those three cells, remove X as a candidate from all other cells in B.
Example: In column 3, digit 3 must be in box 1. Therefore, 3 cannot be a candidate of any other cell in the same box.
Detailed explanations: sudoku.com, sudokuwiki.org, sudopedia.org, HoDoKu.
Practice puzzle: 1.
Common Peer Elimination
Summary: Putting digit X in a cell eliminates X as a candidate from another house, so it's not a valid candidate for that cell.
This technique is the general version of Locked Candidate Pairs. It is more common in variants like Anti Knight and Diagonal because Classic has more specialized techniques.
Detailed explanations: sudopedia.org.
X-Wing
Summary: Find rows where digit X is a candidate in only two cells. If there is a pair of rows where the cells are in the same two columns, remove X as a candidate from all other cells in those columns.
It also works the other way around (columns and rows).
Detailed explanations: sudoku.com, sudokuwiki.org, sudopedia.org, HoDoKu.
XY-Wing
Also known as: Y-Wing, Bent Triples.
Summary: Cell with candidates XY sees two cells with candidates XZ and YZ. Remove Z as a candidate from every cell that sees both cells XZ and YZ.
Detailed explanations: sudopedia.org, sudokuwiki.org, HoDoKu.
Practice puzzle: 1.
Common Peer Elimination (Kropki)
Summary: Only applies to Kropki puzzles. It is a combination of Common Peer Elimination and Kropki Dot Chain Logic.
If all chain combinations eliminate X from cell Y then eliminate it.
Common Peer Elimination (Arrow)
Summary: Only applies to Arrow puzzles. It is a combination of Common Peer Elimination and Arrow Candidates.
If all arrow combinations eliminate X from cell Y then eliminate it.
Turbot Fish
Summary: For a digit X there are 2 strong links (A-B, C-D) and one of their ends see each other (let's assume they are A and B). You can remove X as a candidate from all cells that see both C and D.
There are 3 subtypes of Turbot Fish: Skyscrapers, 2-String Kites and Empty Rectangles.
A Turbot Fish in a particular type of X-Cycle.
Detailed explanations: sudopedia.org, HoDoKu.
Practice puzzle: 1.
Empty Rectangle
Summary: In a box, each of digit X's candidate cells are either on row R or col C.
Detailed explanations: sudopedia.org, HoDoKu, sudokuwiki.org.
Nishio Forcing Chains
Summary: Remove candidate X from a cell because putting digit X in it leads to an invalid grid state.
Detailed explanations: sudokuwiki.org.
Practice puzzle: 1.