Platon Sudoku · Sudoku Study
XY-Wing · Step-by-step example
A two-candidate pivot {X,Y} sees two wings {X,Z} and {Y,Z}. The wings may connect through a box, a row, or a column. Remove the shared third digit from a candidate that sees both wings.
This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.
View on Google PlayRecognize the pattern
A two-candidate pivot {X,Y} sees two wings {X,Z} and {Y,Z}. The wings may connect through a box, a row, or a column.
How to find it
Find a two-candidate pivot, then two other pairs that each share one different pivot digit and the same third digit.
What it allows
Remove the shared third digit from a candidate that sees both wings.
Avoid the mix-up
The pivot itself must have exactly two candidates. The target must see both wings; seeing only the pivot is insufficient.
Step-by-step example · Row link
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 · Find the pivot and wings
R5C8 is the pivot with candidates 4, 7. It sees the two wings: R4C9 with 6, 7, and R5C2 with 4, 6.
Step 2 · Find the shared target
Both wings contain 6. Every target (R4C2=6) sees both wings, so it is their shared target for candidate 6.
Step 3 · Case 1: R5C8 is 4
If R5C8=4, R5C2 cannot be 4 and must be 6.
Step 4 · Case 1: remove target 6
Every target (R4C2=6) sees R5C2, which is 6 in this case. The target therefore cannot be 6.
Step 5 · Case 2: R5C8 is 7
If R5C8=7, R4C9 cannot be 7 and must be 6.
Step 6 · Case 2: remove target 6
Every target (R4C2=6) sees R4C9, which is 6 in this case. The target therefore cannot be 6.
Step 7 · Combine the two cases
The pivot can only be 4, 7. In either case one wing is 6, so remove R4C2=6.
What it allows
The pivot can only be 4, 7. In either case one wing is 6, so remove R4C2=6.
Step-by-step example · Column link
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 · Find the pivot and wings
R2C2 is the pivot with candidates 7, 8. It sees the two wings: R2C3 with 4, 8, and R4C2 with 4, 7.
Step 2 · Find the shared target
Both wings contain 4. Every target (R3C2=4) sees both wings, so it is their shared target for candidate 4.
Step 3 · Case 1: R2C2 is 7
If R2C2=7, R4C2 cannot be 7 and must be 4.
Step 4 · Case 1: remove target 4
Every target (R3C2=4) sees R4C2, which is 4 in this case. The target therefore cannot be 4.
Step 5 · Case 2: R2C2 is 8
If R2C2=8, R2C3 cannot be 8 and must be 4.
Step 6 · Case 2: remove target 4
Every target (R3C2=4) sees R2C3, which is 4 in this case. The target therefore cannot be 4.
Step 7 · Combine the two cases
The pivot can only be 7, 8. In either case one wing is 4, so remove R3C2=4.
What it allows
The pivot can only be 7, 8. In either case one wing is 4, so remove R3C2=4.
Step-by-step example · Row and 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 · Find the pivot and wings
R3C4 is the pivot with candidates 2, 6. It sees the two wings: R3C9 with 1, 6, and R9C4 with 1, 2.
Step 2 · Find the shared target
Both wings contain 1. Every target (R9C9=1) sees both wings, so it is their shared target for candidate 1.
Step 3 · Case 1: R3C4 is 2
If R3C4=2, R9C4 cannot be 2 and must be 1.
Step 4 · Case 1: remove target 1
Every target (R9C9=1) sees R9C4, which is 1 in this case. The target therefore cannot be 1.
Step 5 · Case 2: R3C4 is 6
If R3C4=6, R3C9 cannot be 6 and must be 1.
Step 6 · Case 2: remove target 1
Every target (R9C9=1) sees R3C9, which is 1 in this case. The target therefore cannot be 1.
Step 7 · Combine the two cases
The pivot can only be 2, 6. In either case one wing is 1, so remove R9C9=1.
What it allows
The pivot can only be 2, 6. In either case one wing is 1, so remove R9C9=1.
Practice
This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.
View on Google Play