Naked Pair and Hidden Pair: differences, examples and method

Naked Pair and Hidden Pair are two essential techniques for moving from easy Sudoku to medium Sudoku.

Both work with pairs, but they do it differently. In Naked Pair, the pair is visible in the cells: two cells contain only the same two candidates. In Hidden Pair, the pair is recognized by starting from the numbers: two numbers can go only in the same two cells of a specific area.

Understanding the difference clearly prevents a lot of confusion. The two techniques look similar, but they lead to different eliminations and require a different point of view.

In this guide, we will see the differences between Naked Pair and Hidden Pair, with examples and a practical method for recognizing them during a game.

Pairs are important because they help restrict the possibilities in the grid.

In Sudoku, you do not always immediately find a number to place. Often you first need to eliminate impossible candidates. Pairs are useful exactly for this: they identify situations where two cells or two numbers are linked in a precise way.

Even if a pair does not immediately tell you which number goes in which cell, it still gives you very useful information. You know that certain numbers are reserved for certain positions, so you can either eliminate them from other cells or remove unrelated candidates from the involved cells.

These eliminations can unlock later moves.

Naked Pair is a visible pair because it is recognized by looking directly at the candidates in the cells.

If two cells in the same row, column or box contain exactly the same two candidates, those two cells form a Naked Pair.

For example, two cells in the same row both have only {3,8}. This means that 3 and 8 must occupy those two cells. As a result, you can eliminate 3 and 8 from the other cells in the row.

Naked Pair starts from the cells and produces eliminations on the other cells in the same unit.

Hidden Pair is a hidden pair because it is not immediately visible by looking only at the cells.

In this case, you need to observe a unit and ask yourself where the missing numbers can go. If two numbers can appear only in the same two cells, then those cells are reserved for those two numbers.

For example, in a box, numbers 2 and 9 appear as candidates only in cells A and B. Even if A and B contain other candidates, they must contain 2 and 9. The other candidates in A and B can be eliminated.

Hidden Pair starts from the numbers and produces eliminations inside the two involved cells.

The most important difference is the question you ask yourself.

With Naked Pair you ask: “Are there two cells in the same unit with exactly the same two candidates?”.

With Hidden Pair you ask: “Are there two numbers that, in this unit, can go only in the same two cells?”.

In the first case you look at the cells. In the second, you look at the distribution of the numbers.

This difference completely changes how you analyze the grid. That is why it is useful to train the two techniques separately before using them together.

To understand whether you are using Naked Pair or Hidden Pair, look at where the reasoning starts.

Then look at where the elimination happens:

• with Naked Pair, you eliminate outward, from the other cells of the unit;
• with Hidden Pair, you eliminate inward, from the two involved cells.

The eliminations are different too.

With Naked Pair, you eliminate the pair candidates from the other cells in the same unit.

With Hidden Pair, you eliminate unrelated candidates from the two cells of the pair.

For example, if you have a Naked Pair {4,7} in a row, you eliminate 4 and 7 from the other cells in the row. If you have a Hidden Pair made of numbers 4 and 7 in two cells, you eliminate from those two cells all candidates other than 4 and 7.

This is the most important rule to remember in order to apply the two techniques correctly.

Imagine a row with these empty cells:

• cell A: {1,6};
• cell B: {1,6};
• cell C: {1,4,6};
• cell D: {4,8}.

Cells A and B form a Naked Pair. You can eliminate 1 and 6 from cell C. Cell C is left with the only candidate 4.

Now imagine instead a box where numbers 2 and 5 appear as candidates only in cells E and F:

• cell E: {2,5,7};
• cell F: {2,5,9};
• in the other cells of the box, 2 and 5 do not appear as candidates.

In this case E and F form a Hidden Pair. You can eliminate 7 from E and 9 from F, leaving both cells with {2,5}.

The two examples show the practical difference: with Naked Pair you clean the other cells, while with Hidden Pair you clean the cells of the pair.

To practice pairs, start with Naked Pair. It is easier to see because the cells contain exactly two candidates.

When you feel confident, move on to Hidden Pair. Choose a row, column or box and observe where the missing numbers appear. If two numbers appear only in the same two cells, you have found a hidden pair.

A good exercise is to solve medium Sudoku with visible candidates and stop whenever you cannot find immediate moves. At that point, try to look first for Naked Pair and then for Hidden Pair.

On Sudoku Arena, when you receive a hint based on a pair, try to understand whether the reasoning starts from the cells or from the numbers. This helps you distinguish the two techniques.

Naked Pair and Hidden Pair are two intermediate techniques based on pairs.

Naked Pair is recognized by starting from the cells: two cells in the same unit contain only the same two candidates. It lets you eliminate those candidates from the other cells of the unit.

Hidden Pair is recognized by starting from the numbers: two numbers can go only in the same two cells of a unit. It lets you eliminate from those two cells all candidates unrelated to the pair.

Understanding this difference makes medium Sudoku easier to handle and prepares you for the next techniques.