Intermediate Sudoku Techniques, Part 1: Looking for Number Pairs

Step 1: How to Identify a Naked Pair

A Naked Pair is the most straightforward type of number pair to spot. It consists of two cells within the same row, column, or box that contain exactly the same two candidate digits, and no other candidates. For example, if two cells in a column have the candidates {2, 5} and {2, 5}, you have found a Naked Pair. The logic is sound: those two digits must occupy those two cells, though their exact order is still unknown.

• Focus on units (rows, columns, boxes) where many cells already have few candidates. This is where Naked Pairs are most likely to form.
• Don't overlook pairs that involve a cell you just solved. A new placement can suddenly create a pair in a related unit.

Step 2: How to Spot a Hidden Pair

A Hidden Pair is more subtle but equally powerful. It occurs when two candidate digits appear only in the same two cells of a unit, but those cells also contain other, extra candidates. The 'hidden' part means the pattern is concealed by the clutter of other numbers. For instance, in a row, imagine digits 3 and 9 appear only in cells A and B. If cell A has candidates {1, 3, 9} and cell B has candidates {3, 7, 9}, then 3 and 9 form a Hidden Pair.

• To find Hidden Pairs, scan each unit and look for any two digits that appear as candidates in only two cells. This is a counting exercise.
• Once identified, you must 'clean up' the cells. Remove all candidates other than the pair from those two cells, turning the Hidden Pair into a Naked Pair.

Step 3: Systematically Scan Rows, Columns, and Boxes

Effective pair hunting requires a methodical approach. Scan each row, column, and 3x3 box individually. For Naked Pairs, visually look for two cells with identical double candidates. For Hidden Pairs, mentally note where each candidate digit (1-9) appears in the unit. Count how many cells contain each digit as a candidate. If you find two digits that are candidates in the same two cells and only those two cells, you've found a Hidden Pair. For example, in a row, if only cells R5C2 and R5C7 contain the digits 3 and 9 as possibilities, then {3,9} is a Hidden Pair in those cells, regardless of what other candidates are present.

• Start your scan with the most constrained units, like rows or boxes that are nearly full. They often reveal pairs.
• Use pencil marks! Accurate candidate notation is non-negotiable for seeing these patterns, especially Hidden Pairs.

Step 4: Making the Correct Eliminations

Correctly applying the elimination is the final, crucial step. For a Naked Pair in a row, eliminate its two digits from all other cells in that row. The same logic applies to columns and boxes. For a Hidden Pair, your first eliminations are internal: remove all other candidates from the two cells forming the pair. This often creates a cascade, as those cleaned cells may now form other patterns like a Pointing Pairs or a Naked Single. A common mistake is trying to eliminate the pair's digits from outside the unit. Remember, the eliminations are confined to the unit (row, column, or box) where the pair was found. If two cells share a row and a box, you can make eliminations in both the row and the box, but not in a column they don't fully share.