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X-Wing

X-WingSTEP 0/3

Introduction

The X-Wing strategy comes into play when basic block techniques are no longer enough. It is an advanced technique that allows you to eliminate digits from notes by using the rule of a perfect rectangle on the board.

We look for two parallel lines (for example, two rows) in which a specific digit can appear exactly twice.
Most importantly, these four positions must line up perfectly vertically, forming the corners of a rectangle (sharing the same two columns).

The name comes from the X shape formed by the potential solution lines crossing diagonally. Let's see how it works in a concrete example!

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X-WingSTEP 1/3

Checking the Constraints

Let's analyze the notes for a selected digit - suppose it is the digit 4. We are looking for rows where this digit has a very limited number of positions.

Candidate 4 appears in exactly two places: Row 2, Column 3 and Row 2, Column 8.
We scan the board further and notice the same situation in Row 6 - candidate 4 can also go only in Column 3 or Column 8.
In this way, we have located four cells that form the corners of our rectangle.

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X-WingSTEP 2/3

Finding the Pattern

We have discovered the perfect relationship. Since in Rows 2 and 6 the digit 4 must appear in Column 3 or 8, we have a closed X-Wing pattern.

If the 4 in Row 2 goes into Column 3, then the 4 in Row 6 must automatically go into Column 8 (the diagonal arrangement).
If, on the other hand, we choose Column 8 in Row 2, the 4 in Row 6 is forced into Column 3.

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X-WingSTEP 3/3

Analysis

Regardless of which of these two combinations is true, the conclusion is undeniable: Columns 3 and 8 will have their 4s "reserved" exactly at these positions.

This means that the digit 4 cannot appear anywhere else along the entire length of Columns 3 and 8, except for our four rectangle corners.

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