Platon Sudoku · Sudoku Study

X-Wing · Step-by-step example

For one digit, two rows each have possible positions only in the same two columns. The row and column roles can be reversed. Remove that digit from other cells in those two columns, outside the two selected rows.

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

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Recognize the pattern

For one digit, two rows each have possible positions only in the same two columns. The row and column roles can be reversed.

How to find it

Choose a digit and compare rows with exactly two possible cells for it. Look for another row using the same two columns.

What it allows

Remove that digit from other cells in those two columns, outside the two selected rows.

Avoid the mix-up

A rectangle drawn through any four candidates is not enough. Check that the digit has no other possible cell in either selected row. For a column-based X-Wing, check the selected columns instead.

Step-by-step example · Row

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

Each base region (row 4, row 8) has exactly two positions for 1. The four circled candidates align in the same two cover regions (column 2, column 9), forming an X-Wing.

Step 2 · Case 1: occupy both cover regions

Choose R4C2=1 as true. In the same base region (row 4), it rules out R4C9=1; in the same cover region (column 2), it rules out R8C2=1. The other base region (row 8) is then left with R8C9=1, so that corner is forced true. Both cover regions are occupied, excluding the targets (R1C2=1, R7C2=1).

Step 3 · Case 2: occupy both cover regions

Choose R4C9=1 as true. In the same base region (row 4), it rules out R4C2=1; in the same cover region (column 9), it rules out R8C9=1. The other base region (row 8) is then left with R8C2=1, so that corner is forced true. Both cover regions are occupied, excluding the targets (R1C2=1, R7C2=1).

Step 4 · Conclusion

In either complete pairing, the two 1 placements from the base regions (row 4, row 8) occupy both cover regions (column 2, column 9), one in each. Therefore remove R1C2=1, R7C2=1 outside the bases.

What it allows

In either complete pairing, the two 1 placements from the base regions (row 4, row 8) occupy both cover regions (column 2, column 9), one in each. Therefore remove R1C2=1, R7C2=1 outside the bases.

X-Wing · Remove that digit from other cells in those two columns, outside the two selected rows.

Step-by-step example · Column

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

Each base region (column 3, column 5) has exactly two positions for 1. The four circled candidates align in the same two cover regions (row 2, row 4), forming an X-Wing.

Step 2 · Case 1: occupy both cover regions

Choose R2C3=1 as true. In the same base region (column 3), it rules out R4C3=1; in the same cover region (row 2), it rules out R2C5=1. The other base region (column 5) is then left with R4C5=1, so that corner is forced true. Both cover regions are occupied, excluding the targets (R4C4=1, R4C7=1, R4C9=1).

Step 3 · Case 2: occupy both cover regions

Choose R4C3=1 as true. In the same base region (column 3), it rules out R2C3=1; in the same cover region (row 4), it rules out R4C5=1. The other base region (column 5) is then left with R2C5=1, so that corner is forced true. Both cover regions are occupied, excluding the targets (R4C4=1, R4C7=1, R4C9=1).

Step 4 · Conclusion

In either complete pairing, the two 1 placements from the base regions (column 3, column 5) occupy both cover regions (row 2, row 4), one in each. Therefore remove R4C4=1, R4C7=1, R4C9=1 outside the bases.