Everydoku

X-Wing

A single-digit pattern that opens the door to advanced techniques. If in two rows a digit can go in exactly two cells each, and those cells sit in the same two columns, the four cells form a rectangle. In those two columns, the digit can be removed from every other cell.

Why it works

As in the example below, say the digit 3 can go only in column 3 or column 9 in row 6, and only in column 3 or column 9 in row 9 too. If row 6's 3 is in column 3, then row 9's 3 must be in column 9 (column 3 already has one). If row 6's 3 is in column 9, row 9's is in column 3. Either way, column 3 and column 9 each get their 3 within these two rows. So no other row can have 3 in those columns. The answer is always one of the rectangle's two diagonals, which form an X: hence the name.

On a real board

Only the candidates for 3 are shown. In row 6 and row 9, 3 fits only in column 3 and column 9 (circled). So 3 comes off the rest of both columns (red). Play this board โ†’

This is a 9ร—9 ยท Expert board, filled as far as naked and hidden singles go. Only the candidates for 3 are shown.

  1. Look at where 3 can go in row 6 and row 9. In both rows, only the cells in column 3 and column 9 are possible (circled).
  2. The four cells form a rectangle. The two rows' 3s sit on one of its diagonals.
  3. So remove 3 from the rest of column 3 and column 9. On this board that is 5 cells: row 3, column 3, row 4, column 3, row 5, column 3, row 7, column 3 and row 4, column 9.
  4. After that, the outlined cell row 3, column 2 becomes 3, as a hidden single in row 3.

Columns work too

If in two columns a digit fits only in the same two rows, the same logic removes it from the rest of those two rows. Check both directions when you scan.

Spotting it

  1. Pick a digit. Digits with few copies on the board so far are the most likely to form an X-Wing.
  2. For each row, count the cells where that digit is a candidate. Note the rows with exactly two.
  3. Among those rows, look for two whose two cells are in the same columns.
  4. Then scan those two columns for candidates to remove. If there are none, the X-Wing is real but useless.
Don't confuse it with locked candidates. If the rectangle's four cells sit inside just two boxes, locked candidates usually explain the same removal. The X-Wing earns its keep when the four cells are spread over four different boxes, as in the example above.

Going further

Widen the X-Wing to three rows and three columns and you get the Swordfish; four and four make a Jellyfish. The principle is the same: if in n rows a digit's places all lie within the same n columns, remove it from the other cells of those columns.

When you get stuck on a 9ร—9 Expert or 16ร—16 Master board, think of this article and the hidden pair. If you are still stuck, use a hint. Everydoku explains moves that the first four techniques (naked single to naked pair) can find; for harder spots it reveals the cell with the fewest candidates.

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