Platon Sudoku · Sudoku Study

Skyscraper · Step-by-step example

Two strong links for one digit lie on parallel rows or columns. One end of each link shares a crossing line. Remove the digit from any cell that sees both unaligned ends.

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Recognize the pattern

Two strong links for one digit lie on parallel rows or columns. One end of each link shares a crossing line.

How to find it

Find two rows with exactly two candidates for one digit. Align one candidate from each row in a column, then inspect the other two ends.

What it allows

Remove the digit from any cell that sees both unaligned ends.

Avoid the mix-up

The aligned ends need not be in the same box. Each base line must have exactly two candidates; a target must see both unaligned ends.

Step-by-step example · Row

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 two strong links

For 8, row 5 has only R5C4 and R5C1, while row 7 has only R7C5 and R7C1. Each pair is a strong link: if one end is false, the other is true.

Step 2 · Connect the links into a Skyscraper

R5C1 and R7C1 see each other in column 1, so they cannot both be 8. They are the two base ends; R5C4 and R7C5 are the two roofs. This weak link between the base ends connects the two strong links into a Skyscraper.

Step 3 · Follow the chain to the other roof

If roof R5C4 is not 8, row 5 forces R5C1 to be 8. That rules out R7C1 in column 1, so row 7 forces the other roof R7C5 to be 8.

Step 4 · At least one roof is true

If R5C4 is 8, the claim is immediate; if not, the chain forces R7C5 to be 8. Therefore at least one roof is 8. Every target (R8C4) sees both roofs, so none can be 8.

Step 5 · Remove the target candidates

At least one of the two roofs is 8, and every target (R8C4) sees both. Remove candidate 8 from these targets.

What it allows

At least one of the two roofs is 8, and every target (R8C4) sees both. Remove candidate 8 from these targets.

Skyscraper · Remove the digit from any cell that sees both unaligned ends.

Step-by-step example · 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 two strong links

For 1, column 2 has only R5C2 and R2C2, while column 8 has only R6C8 and R2C8. Each pair is a strong link: if one end is false, the other is true.

Step 2 · Connect the links into a Skyscraper

R2C2 and R2C8 see each other in row 2, so they cannot both be 1. They are the two base ends; R5C2 and R6C8 are the two roofs. This weak link between the base ends connects the two strong links into a Skyscraper.

Step 3 · Follow the chain to the other roof

If roof R5C2 is not 1, column 2 forces R2C2 to be 1. That rules out R2C8 in row 2, so column 8 forces the other roof R6C8 to be 1.

Step 4 · At least one roof is true

If R5C2 is 1, the claim is immediate; if not, the chain forces R6C8 to be 1. Therefore at least one roof is 1. Every target (R6C3) sees both roofs, so none can be 1.