Hidden Pairs Explained with Worked Examples

Why Hidden Pairs Are Often Overlooked

Most players get stuck because they scan cells for patterns. They look for a cell with only two candidates or a clear Naked Pair. The Hidden Pair technique requires you to flip your perspective. Instead of scanning cells, you scan digits. For each digit from 1 to 9, you must check how many and which cells in a unit (row, column, or 3x3 box) can possibly contain it. If you find two digits that share the same two possible cells, and only those two cells, you have found a Hidden Pair.

This digit-by-digit analysis is how you spot patterns that are 'hidden' among other candidate numbers. The technique is a direct counterpart to finding a Hidden Single, but it involves two digits instead of one. The core skill is systematic digit tracking, not just pattern recognition in individual cells.

• To practice, pick a single row. Write down the candidate list for every empty cell in that row.
• Then, for digits 1-9, count and note which cells can hold each digit. Look for any two digits that appear in exactly the same two cells.

Worked Example 1: Finding a Hidden Pair in a Row

Let's examine Row 5. After basic candidate marking, the empty cells have these possible numbers:

R5C2: {1,4,6,8}

R5C4: {1,6}

R5C6: {1,6}

R5C7: {4,8}

R5C8: {6}

R5C9: {1,6}

Now, scan digit by digit across this row. Where can digit 4 go? It appears only in R5C2 and R5C7. Where can digit 8 go? It also appears only in R5C2 and R5C7. No other cell in Row 5 can contain a 4 or an 8.

This means the digits 4 and 8 form a Hidden Pair in cells R5C2 and R5C7. The logic is clear: these two numbers must occupy these two cells, though we don't yet know which is which. Because they must go there, all other candidates in those two cells are impossible and can be removed.

We eliminate 1 and 6 from R5C2, changing it to {4,8}. We also check R5C7, which is already {4,8}, so no change is needed there. This cleanup is crucial. It simplified R5C2 and may now create new Naked Singles or other patterns in the row.

Worked Example 2: Finding a Hidden Pair in a 3x3 Box

Let's look at Box 5 (the center box of the grid). The candidate lists for its empty cells are:

R4C4: {3,6,9}

R4C5: {1,2,9}

R4C6: {1,2,7}

R5C4: {3,6,9}

R5C5: {1,2,7}

R5C6: {1,2,7}

R6C4: {1,2}

R6C5: {1,2,7}

R6C6: {1,2,7}

Perform the digit scan. Where can digit 3 go in this box? Only in R4C4 and R5C4. Where can digit 6 go in this box? Only in R4C4 and R5C4. Digits 3 and 6 are confined to the same two cells.

Thus, {3,6} is a Hidden Pair in cells R4C4 and R5C4. Since 3 and 6 must be placed in these two cells, the candidate '9' cannot be correct in either. We eliminate 9 from both R4C4 and R5C4.

After elimination, R4C4 becomes {3,6} and R5C4 becomes {3,6}. This not only simplifies these cells but also affects the columns and rows they are in. It’s a classic example of how a box-focused Hidden Pair can interact with Pointing Pairs logic in the columns above and below.

How to Practice Spotting Hidden Pairs

The best way to master this is deliberate practice. Use the candidate note feature on SudokuHint.com. After filling in all possible candidates for a puzzle, don't just look for the next obvious move. Pick a unit that seems crowded.

Methodically list, either mentally or on paper, the possible cells for each digit 1-9 in that unit. Look for the telltale sign: two digits that have the exact same two-cell 'footprint'. When you find them, you can confidently remove all other numbers from those two cells.

Remember, a Hidden Pair is different from a Naked Pair. A Naked Pair is visible in the candidate lists of two cells (e.g., both cells show only {4,8}). A Hidden Pair is buried among other candidates, so you must deduce its existence by analyzing digit placement.

• Start by practicing in rows and columns, as they are linear and easier to scan than boxes.
• If a unit has many cells with long candidate lists, it's a prime hunting ground for Hidden Pairs.