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Hard

X-Wing

An X-Wing is the first technique most solvers hit that looks across the whole board rather than one unit at a time. Pick a digit, and find two rows where its only remaining candidates line up in the exact same two columns — four cells forming a rectangle. That rectangle forces the digit out of the rest of those two columns.

Why it works

Each of the two rows needs the digit somewhere in those two columns. Whichever column takes it in the first row, the digit has to fall in the other column for the second row — since a column can't repeat a digit. Between the two rows, both columns end up used, so no other row can place that digit in either column.

Worked example

9
7
4
2
1
8
7
5
2
6
1
9
4
5
4
5
7
9
9
2
1
8
3
4
5
9
5
7
Step 1 of 3

Find the pattern

In rows 1, 6, 4 can only go in columns 1, 2. The four corner cells form a rectangle.

9
7
4
2
1
8
7
5
2
6
1
9
4
5
4
5
7
9
9
2
1
8
3
4
5
9
5
7
Step 2 of 3

Why it works

Each row needs one of the two corner cells to hold it, and each of those columns can only have it once. Either way the digit lands in both columns.

9
7
4
2
1
8
348
1489
7
5
2
6
1
9
4
5
4
5
7
9
9
2
1
8
3
4
5
9
5
7
Step 3 of 3

Eliminate

4 can be crossed out of the other cells in columns 1, 2.

Tips

KaizenDoku spots every one of these patterns automatically after each game, and shows you exactly where you used them on your own board.

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