Platon Sudoku · Sudoku Study
X-Chain · Step-by-step example
A chain of one digit alternates verified strong and weak links, making at least one end true. Eliminate the digit from any target that sees both endpoints.
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 chain of one digit alternates verified strong and weak links, making at least one end true.
How to find it
Start at a strong link for one digit, alternate link types without skipping a candidate, and test targets visible from both ends.
What it allows
Eliminate the digit from any target that sees both endpoints.
Avoid the mix-up
A strong link needs exactly two candidates in its region; a weak link only says both ends cannot be true.
Step-by-step example · Short chain
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
Use the verified candidates shown here. Earlier valid removals remain in effect.
Step 2 · Reasoning
Branch 1: suppose R5C8=2 is false.
Step 3 · Reasoning
R5C8=2 is false. Together these two sides contain every remaining option in row 5. Therefore R5C4=2 must be true.
Step 4 · Reasoning
R5C4=2 is true. Remove R2C4=2.
Step 5 · Reasoning
R2C4=2 is false. Together these two sides contain every remaining option in box 2. Therefore R1C5=2 must be true.
Step 6 · Reasoning
R1C5=2 is true. Remove R1C9=2.
Step 7 · Reasoning
R1C9=2 is false, so R8C9=2 is forced in column 9. Every target sees R8C9=2, so cross out R7C8=2, R8C8=2.
Step 8 · Withdraw the previous rectangle filling
Withdraw this assumption and its consequences. Return to the unchanged candidate snapshot before examining the next possibility.
Step 9 · Reasoning
Set R5C8=2. Every target sees it, so cross out R7C8=2, R8C8=2.
Step 10 · Conclusion
The two endpoint cases exhaust all possibilities and both cross out R7C8=2, R8C8=2. Withdraw the temporary states, then remove these candidates.
What it allows
The two endpoint cases exhaust all possibilities and both cross out R7C8=2, R8C8=2. Withdraw the temporary states, then remove these candidates.
Step-by-step example · Medium chain
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
Use the verified candidates shown here. Earlier valid removals remain in effect.
Step 2 · Reasoning
Branch 1: suppose R1C3=7 is false.
Step 3 · Reasoning
R1C3=7 is false. Together these two sides contain every remaining option in row 1. Therefore R1C7=7 must be true.
Step 4 · Reasoning
R1C7=7 is true. Remove R8C7=7.
Step 5 · Reasoning
R8C7=7 is false. Together these two sides contain every remaining option in row 8. Therefore R8C8=7 must be true.
Step 6 · Reasoning
R8C8=7 is true. Remove R5C8=7.
Step 7 · Reasoning
R5C8=7 is false. Together these two sides contain every remaining option in box 6. Therefore R4C9=7 must be true.
Step 8 · Reasoning
R4C9=7 is true. Remove R4C5=7.
Step 9 · Reasoning
R4C5=7 is false, so R2C5=7 is forced in column 5. Every target sees R2C5=7, so cross out R2C3=7.
Step 10 · Withdraw the previous rectangle filling
Withdraw this assumption and its consequences. Return to the unchanged candidate snapshot before examining the next possibility.
Step 11 · Reasoning
Set R1C3=7. Every target sees it, so cross out R2C3=7.
Step 12 · Conclusion
The two endpoint cases exhaust all possibilities and both cross out R2C3=7. Withdraw the temporary states, then remove these candidates.
What it allows
The two endpoint cases exhaust all possibilities and both cross out R2C3=7. Withdraw the temporary states, then remove these candidates.
Step-by-step example · Long chain
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
Use the verified candidates shown here. Earlier valid removals remain in effect.
Step 2 · Reasoning
Branch 1: suppose R1C5=9 is false.
Step 3 · Reasoning
R1C5=9 is false. Together these two sides contain every remaining option in row 1. Therefore R1C3=9 must be true.
Step 4 · Reasoning
R1C3=9 is true. Remove R3C1=9.
Step 5 · Reasoning
R3C1=9 is false. Together these two sides contain every remaining option in column 1. Therefore R5C1=9 must be true.
Step 6 · Reasoning
R5C1=9 is true. Remove R6C3=9.
Step 7 · Reasoning
R6C3=9 is false. Together these two sides contain every remaining option in row 6. Therefore R6C7=9 must be true.
Step 8 · Reasoning
R6C7=9 is true. Remove R5C8=9.
Step 9 · Reasoning
R5C8=9 is false. Together these two sides contain every remaining option in column 8. Therefore R9C8=9 must be true.
Step 10 · Reasoning
R9C8=9 is true. Remove R9C2=9.
Step 11 · Reasoning
R9C2=9 is false, so R8C2=9 is forced in column 2. Every target sees R8C2=9, so cross out R8C5=9.
Step 12 · Withdraw the previous rectangle filling
Withdraw this assumption and its consequences. Return to the unchanged candidate snapshot before examining the next possibility.
Step 13 · Reasoning
Set R1C5=9. Every target sees it, so cross out R8C5=9.
Step 14 · Conclusion
The two endpoint cases exhaust all possibilities and both cross out R8C5=9. Withdraw the temporary states, then remove these candidates.
What it allows
The two endpoint cases exhaust all possibilities and both cross out R8C5=9. Withdraw the temporary states, then remove these candidates.
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