Sudoku-YAdvanced
XY-Wing: two pivot cases, one shared elimination
Two short conditional paths establish the same elimination. Neither path needs to be chosen as the pivot’s answer.
Practise on a board ↓LOOK · TRY · UNDERSTAND
Try it and see why
Two paths, one elimination
B2 is the pivot. Both B8 and H2 see it. All three cells have the complete notes shown.
Our own partial teaching board, not a full puzzle. Large digits are placed values; small digits are candidates. Dots mean the cell is not described here. Complete candidate lists are part of the stated scenario, not calculated from the dots.
Green outline = evidence · Purple “try” = an assumption · Crossed out = removed candidate
Try both B2 values, then remove the 5 that both paths rule out.
Select a cell, then tap a candidate below.
Removed 0/1
See the reasoning
B2=2 forces B8=5; B2=7 forces H2=5. H8 sees both wings, so cannot be 5. E5 does not see both wings.
Digit set 1/9 · A different digit set in the same pattern, not a new full puzzle.
Read the source principles: HoDoKu — Wings
Three bivalue cells
A pivot {x,y} sees wings {x,z} and {y,z}. Seeing means sharing a row, column or box. Pivot x forces the first wing to z; pivot y forces the second. A target that sees both wings cannot contain z.
HoDoKu — Wings · SudokuWiki — Y-Wing
Crossed-out digits are eliminations. Check the full conditions in the worked example below.
Follow B2, B8 and H2
Use pivot B2={2,7}, wing B8={2,5} and wing H2={5,7}. B2=2 forces B8=5; B2=7 forces H2=5. H8 sees B8 through column 8 and H2 through row H, so remove 5 from H8. Seeing the pivot is unnecessary for the target.
Try before revealing
Can a target seeing only one wing lose 5 by this argument?
Show explanation
No. The other case could place 5 in the wing it cannot see. Both wing relationships are required.
Check the missing conditions
A third pivot candidate introduces an uncovered case. An extra wing candidate may prevent that wing from being forced to 5. Three cells arranged like a letter Y are not sufficient evidence.
In Sudoku-Y
The scanner identifies the pivot, shows wing candidates and explains both paths on your current board. It proves an elimination, not the pivot’s value, and does not create a what-if case for you.
References and further reading
Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.