Hidden Pair in Sudoku: the hidden pair

Hidden Pair is an intermediate Sudoku technique that requires a little more attention than Naked Pair.

In a Naked Pair, the pair is obvious because two cells contain exactly the same two candidates. In a Hidden Pair, instead, the pair is hidden inside cells that may also have other candidates.

The idea is this: if two numbers can appear only in the same two cells of a row, column or box, then those two cells must be reserved for those two numbers. All other candidates present in those two cells can be eliminated.

In this guide, we will see how to recognize a Hidden Pair, how to distinguish it from a Naked Pair and how to use it to simplify the grid.

A Hidden Pair is formed by two numbers that, within the same unit - row, column or box - can be placed only in the same two cells.

The involved cells may also contain other candidates. That is exactly why the pair is “hidden”: it is not immediately visible by looking only at the cells, because the two numbers are mixed with other possibilities.

When you identify a Hidden Pair, you can eliminate from the two involved cells all candidates that are not part of the pair.

For example, if in a row the numbers 4 and 8 can go only in two specific cells, those two cells must contain 4 and 8. If those cells also include candidates such as 2 or 6, those can be eliminated.

The difference between Naked Pair and Hidden Pair is the point of view.

With a Naked Pair, you start from the cells: you find two cells with exactly the same two candidates. Then you eliminate those candidates from the other cells in the same unit.

With a Hidden Pair, you start from the numbers: you find two numbers that, in a certain unit, can go only in the same two cells. Then you eliminate the other candidates from those two cells.

The practical difference is in the eliminations. With Naked Pair you eliminate the pair candidates from the other cells of the unit. With Hidden Pair you eliminate unrelated candidates from the two cells of the pair.

This difference is essential to avoid confusing the two techniques.

To find a Hidden Pair, you need to analyze a row, column or box and observe where the missing numbers can go.

A good method is to choose one unit and check the candidates number by number. If two numbers appear as candidates only in the same two cells of the unit, then you have found a hidden pair.

For example, in a 3×3 box, number 3 appears as a candidate only in cells A and B. Number 7 also appears as a candidate only in cells A and B. This means that A and B must contain 3 and 7.

If A and B also contain other candidates, you can eliminate them.

The difficulty is noticing the pair inside cells that look more complex at first.

Hidden Pair can appear in any Sudoku unit: rows, columns or boxes.

In a row, you look for two numbers that can be placed only in two cells of the row. In a column, you use the same reasoning vertically. In a box, you check the nine cells of the box and verify where the missing numbers can go.

Boxes are often the best place to start because they are more compact areas and visually easier to analyze. Rows and columns, however, are just as important.

Once the pair is found, the rule does not change: the two involved cells must contain those two numbers, so the other candidates can be removed from those cells.

The practical consequence of Hidden Pair is reducing the candidates in the two cells of the pair.

If two cells contain candidates {2,4,8} and {4,8,9}, and in that row the numbers 4 and 8 can go only in those two cells, then the two cells must be reserved for 4 and 8.

You can therefore eliminate 2 from the first cell and 9 from the second. Both cells become {4,8}.

At that point, the pair that was previously hidden becomes visible as a closed pair. Even if you do not yet know which cell will be 4 and which will be 8, you have simplified the grid correctly.

Imagine a 3×3 box with four empty cells:

• cell A: candidates 1, 4 and 6;
• cell B: candidates 2, 4 and 6;
• cell C: candidates 1, 3 and 8;
• cell D: candidates 2, 5 and 9.

In the box, numbers 4 and 6 appear only in cells A and B. This means that A and B must contain exactly 4 and 6.

The other candidates present in A and B are no longer valid. You can eliminate 1 from A and 2 from B.

After the elimination, A and B are left with candidates {4,6}. The hidden pair has become a closed pair: you do not yet know which cell will be 4 and which will be 6, but you know that those two numbers will occupy A and B.

Hidden Pair becomes useful when the grid no longer offers immediate moves.

If you cannot find Naked Single, Hidden Single or Naked Pair, it may be time to analyze the missing numbers in each unit and look for hidden pairs.

This technique is especially useful in medium Sudoku, where cells often have several candidates and solutions are not always visible at a glance.

Learning Hidden Pair also helps improve the way you read the grid: instead of looking only at cells, you begin to follow the distribution of numbers.

Hidden Pair occurs when two numbers can go only in the same two cells of a row, column or box.

The involved cells may have other candidates, but those can be eliminated because the two cells are reserved for the hidden pair.

It is an important intermediate technique, different from Naked Pair but complementary to it. Using it well lets you clean up the grid and prepare new logical moves.