sudokUI › Sudoku techniques › XYZ-Wing
XYZ-Wing in sudoku
bent triple · ALS-XZ · how it fits
A pivot cell with exactly three candidates X, Y and Z sees two bivalue pincer cells, one with candidates X and Z, the other with candidates Y and Z.
Why it works
If the pivot is X or Y, the pincer holding that digit becomes Z; otherwise the pivot itself is Z. At least one of the three cells is therefore Z, so Z is eliminated from every other cell that sees all three.
How to spot it
Find a three-candidate cell, then look in its box and along its row or column for two bivalue cells holding different pairs of its candidates.
Worked example
XYZ-Wing: pivot r2c5 (459) with pincers r3c6 (45) and r7c5 (49). Whichever digit the pivot takes, one of the three cells is 4, so 4 is removed from every cell that sees all three. So 4 is removed from r3c5.
Practise it on a real puzzle. sudokUI generates a puzzle that needs XYZ-Wing and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs XYZ-Wing, the puzzle's difficulty rating grows by 180. Its class is Hard. It is needed in 1 in 33 puzzles that sudokUI generates. How the rating works.