Sudoku Naked Pairs and Naked Triples Explained: Intermediate Techniques with Pointing and Claiming

Intermediate techniques remove candidates

The Hidden Single and Naked Single from the basics of solving sudoku each place one digit. Intermediate techniques don't place a digit by themselves, but they reduce the candidates in other cells. Once candidates are reduced, Hidden Singles and Naked Singles become available again. That is how intermediate puzzles flow.

In the difficulty levels of Sudoku Next-Move Hints, puzzles that need Pointing, Claiming or Naked Pairs are rated Hard, and those that need Hidden Pairs or Naked Triples are rated Advanced. (In Japan, the Naked Pair is known as "yoyaku", a reservation, and the Naked Triple as "sangoku doumei", a three-nation alliance.)

Pointing: when a box's candidates line up in a straight line

If, in some box, a digit's candidates are only in one row (or column), then wherever that digit goes in the box, it will be in that row (column). So the digit can't go anywhere else in that row (column) outside the box. Let's look at the candidates for 5 in the top-right box of a real position.

The candidates for 5 are R1C9 and R3C9, both in column 9. Column 9's 5 will be used inside this box, so you can remove 5 from R7C9 (candidates 5, 7, 8), which is outside the box. Claiming works in the opposite direction: when all of a row's (column's) candidates for a digit fall inside one box, you remove that digit from the box's other cells.

Naked Pair: the same two candidates in two cells

If a row, column or box contains two cells whose only candidates are exactly the same two digits, those two digits are "reserved" for those two cells. Even if you don't know which goes where, they can't go in any other cell. Here are the candidates of the empty cells in column 3 of a real position.

R5C3 and R8C3 form a 5-6 Naked Pair, so you can remove 5 and 6 from R1C3 and R9C3 in the same column. Naked Pairs jump out if you note cells with only two candidates. That is why, when solving on paper, it pays to note digits that can go in only two cells of a box as a pair.

Naked Triple: three digits in three cells

A Naked Triple extends the Naked Pair to three cells. Note that the three cells don't all need to have all three candidates. The pattern holds as long as the three cells' candidates together are only three different digits. In column 7 of a real position, things looked like this.

The three cells 8-9, 5-8 and 5-9 each have only two candidates, but together they cover three digits: 5, 8 and 9. Three cells, three digits, so 5, 8 and 9 are used up in these three cells. Removing 5, 8 and 9 from the other cells in the column leaves R6C7 as 4. By the same logic, there is also a Hidden Triple, where three digits can only go in the same three cells.

Tips for spotting them and the order to look

• Pointing first: in each box, check whether a digit that can go in only 2–3 places lies in a straight line. Easy to spot even without writing all candidates
• Then Naked Pairs: look for cells with two candidates and check for the same combination in the same row, column or box
• For Hidden Pairs, count the places each digit can go in rows, columns and boxes with many empty cells
• Look for Naked Triples in rows, columns and boxes with three or more cells that have 2–3 candidates
• Each time you remove a candidate, go back and check for Hidden Singles and Naked Singles

Sudoku Next-Move Hints looks for the simplest move first, in the order used in this article (Hidden Single → Naked Single → Pointing / Claiming → Naked Pair → Hidden Pair → Naked Triple → Hidden Triple → X-Wing → Swordfish). When the second level of a hint says Naked Pair, the candidates you can remove are shown with their cell positions (and if Show candidates is on, they are struck through in red on the grid), and you can apply them with Remove these candidates. If you are still stuck at the intermediate level, the position may need an X-Wing or a Swordfish.

FAQ

What is a Naked Pair in sudoku?

It is when a row, column or box has two cells whose only candidates are the same two digits. Those two digits are bound to go in those two cells (they are reserved), so you can remove them from the other cells. It is also called a locked pair, and in Japan "yoyaku" (reservation).

Does a Naked Triple need the same three candidates in all three cells?

No. It holds as long as the three cells' candidates together are only three different digits. Three cells like 8-9, 5-8 and 5-9, each with two candidates, still form a Naked Triple.

What is the difference between Pointing and Claiming?

Pointing is when a digit's candidates inside a box lie in one row (column), and you remove the digit from that row (column) outside the box. Claiming is when a digit's candidates in a row (column) fit inside one box, and you remove it from the box's other cells. They just look in opposite directions; both are called locked candidates.

I found a Naked Pair but no digit gets placed. Was it useful?

Yes. Naked Pairs and Naked Triples are techniques for removing candidates, so often no digit is placed right away. After removing them, check whether new Hidden Singles or Naked Singles have appeared in the same row, column or box.