Free printable sudoku, solver and variants

Naked Triple Sudoku

See a naked triple on a real puzzle, or paste your own and find it.

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This naked triple sudoku tool finds the pattern in a puzzle and shows which candidates it removes. This free tool finds naked triples in a 9×9 sudoku and shows exactly which candidates they let you remove. It runs in your browser, needs no sign-up and nothing to install, and nothing is uploaded.

The page opens on Example 1, a real puzzle where a naked triple is the next move. You can also paste your own puzzle to see where the technique works. The board marks each step: yellow cells are the pattern, blue cells are the row, column or box involved, and red circles are the candidates that can be removed. The tool only removes candidates and never places a digit directly, so you can follow the reasoning before any digit is filled in.

Naked triple sudoku example

How to use the Naked Triple Sudoku tool

  1. Open the page. It starts on Example 1, with the first naked triple already marked on the board.
  2. To try another real puzzle, open the menu “Example puzzles” and choose Example 2, 3 or 4. Choosing one starts the search again.
  3. To use your own puzzle, paste or type 81 characters into the “Your own puzzle” box. Use the digits 1 to 9 for given digits and a dot or 0 for each empty cell. Spaces and line breaks are ignored.
  4. Press “Find Naked Triple in my puzzle”. If the text has the wrong length, a character that is not a digit or an empty cell, two equal digits in one row, column or box, or no solution, a red message tells you what to fix.
  5. Read the board and the message. The message gives the number of simpler steps used first, then the exact cells and digits, then what to remove, for example “Remove 1 from R8C4.” R means row and C means column, counted from the top left.
  6. Click “Apply it and find the next one” to remove the red candidates, solve on with the easier techniques, and show the next place a naked triple works. Click “Start over” to go back to the first one.
  7. When no further pattern exists, the message says so and tells you whether the puzzle is now solved.

What is a naked triple in sudoku

A naked triple is a set of three empty cells in the same row, column or box whose candidates together contain exactly three digits. Those three digits must fill the three cells, so they can be removed as candidates from every other empty cell in that unit.

How do you find a naked triple

Start by writing the pencil marks for every empty cell. Then:

  1. Pick a row, column or box.
  2. List its empty cells that have two or three candidates.
  3. Choose three of them and combine their candidates.
  4. If the combined set has exactly three digits, remove those digits from the other cells of that unit.

In Example 1, row 8 holds R8C1 (6, 9), R8C8 (1, 6, 9) and R8C9 (1, 6). Together they hold only 1, 6 and 9. So 1 and 6 are removed from R8C4, and 9 is removed from R8C7. The same works in columns: in Example 2, R2C2, R3C2 and R4C2 hold only 4, 5 and 7 in column 2, so 4 is removed from R6C2.

What is the difference between a naked triple and a hidden triple

In a naked triple, the three cells contain only those three digits among their candidates, and those digits are removed from the rest of the unit. In a hidden triple, three digits can go only in those three cells, so the other candidates are removed from those cells. A naked pair is the two-cell version of a naked triple.

Does every cell of a naked triple contain all three digits

No. The test is that the union of the three cells’ candidates has exactly three digits. Combinations such as 1-2, 2-3 and 1-3 are all valid, as are 1-2-3, 1-2 and 2-3. In Example 1, the cell R8C1 holds only 6 and 9, and it still belongs to the triple.

How often does a naked triple appear

Rarely. On the site’s puzzle generator, 1,500 random single-solution puzzles with 22 to 27 clues were tested, and not graded by difficulty. A naked triple was the next move at some point of the easiest-first solve in 2.5 % of them, about 1 puzzle in 40. Easy and medium puzzles do not need it. It belongs to the Hard level of this site, alongside hidden triples, X-Wing, Y-Wing and Swordfish.

Frequently asked questions

Does the tool fill in the digits for me?

No. It only removes candidates. A digit is placed once a cell has a single candidate left, so you see each removal before any placement follows.

What does “after 29 simpler steps” mean?

The solver uses the easier techniques first, in this order: Naked Single, Hidden Single, Locked Candidates (Pointing and Claiming), Naked Pair and Hidden Pair. The number counts how many of those steps were needed before the naked triple.

Are the removals guesses?

No. Each removal follows from the rules of sudoku. The tool checks all its examples against a brute-force solver, and no removed candidate is the solution digit.

What if my puzzle has no naked triple?

The message then says either that the puzzle is solved with other techniques, or that the 12 techniques cannot finish it and it needs a harder technique or a guess. If the pattern appears earlier but an easier move also works, the tool shows the pattern with a message saying so.

Can I use a newspaper puzzle?

Yes. Copy its 81 cells into the “Your own puzzle” box, using digits for the given numbers and a dot or 0 for empty cells. If the puzzle has more than one solution, the tool adds a note that its moves are still valid logic.