"Hidden Pairs"Technique

What is a "Hidden Pair"?

The "Hidden Pairs" technique is the next level up from "Hidden Singles". It requires players to scan the notes of an entire block, row, or column to find a special pair.

"Hidden" vs. "Obvious" Pairs

An "Obvious Pair" is when two cells have only the same two notes (e.g., {7, 9} and {7, 9}).

A "Hidden Pair" is when two numbers (e.g., '2' and '6') appear as candidates only in two specific cells within a house, but those cells also contain other notes (e.g., {2, 3, 4, 6, 8} and {2, 4, 6, 7}).

The Logic Behind It

If the numbers '2' and '6' only appear in Cell A and Cell B within this block, then Cell A and Cell B must be 2 and 6. Therefore, we can confidently eliminate all other notes from those two cells.

How to Find a Hidden Pair

Let's look at the example in the middle-right 3x3 block.

In this block, we can see the following filled numbers and notes:

• Filled Numbers: 5 (R4C8), 1 (R6C8).
• Notes (Candidates):

  R4C7 = {4, 8, 9}

  R4C9 = {2, 3, 4, 6, 8, 9}

  R5C7 = {3, 4, 7, 8}

  R5C8 = {3, 4, 7, 8}

  R5C9 = {2, 3, 4, 6, 7, 8}

  R6C7 = {3, 4, 7, 8}

  R6C9 = {3, 4, 7, 8, 9}

Step 1: Scan the Block for a Pair

We must scan the notes of all 7 empty cells, looking for two numbers that appear only twice.

Scan for '2': The note '2' only appears in cells R4C9 and R5C9.

Scan for '3': Appears in 5 cells.

Scan for '4': Appears in 6 cells.

Scan for '6': The note '6' only appears in cells R4C9 and R5C9.

Scan for '7': Appears in 4 cells.

Scan for '8': Appears in 6 cells.

Scan for '9': Appears in 3 cells.

Step 2: Lock the Pair

We found our "Hidden Pair": {2, 6}. These two numbers only appear in the same two cells (R4C9 and R5C9). This means these two cells must be 2 and 6.

Step 3: Eliminate Other Notes

Now that we know R4C9 and R5C9 must be 2 or 6, we can remove all the other "victim" notes from those two cells.

• For R4C9: The notes were {2, 3, 4, 6, 8, 9}. We eliminate 3, 4, 8, and 9. The notes become {2, 6}.
• For R5C9: The notes were {2, 3, 4, 6, 7, 8}. We eliminate 3, 4, 7, and 8. The notes become {2, 6}.

By finding this "Hidden Pair", we have successfully cleaned up our notes and created a new "Obvious Pair"!

Master This Scanning Technique

This technique is a major step in solving harder puzzles. It trains your eyes to scan for patterns, not just individual cells.