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ENVI

Skyscraper

N-step reasoningDifficulty

Two parallel strong links share a base, so a cell that sees both tops cannot be d.

Rule

Two rows each with only 2 places for d, one end of each in the same column → remove d from cells that see both other ends.

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Two strong links

Digit 7 has only two places in row 5: r5c7 and r5c3. In row 9 it also has only two: r9c7 and r9c1. Each pair is a strong link: if one cell is not 7, the other certainly is.

The idea

Picture two buildings side by side. In two rows (or two columns), digit d has exactly two places — each row is a strong link. One end of each (the "bases") lines up in the same column, while the other ends (the "tops") do not.

The two bases share a column, so they cannot both be d; at least one base is not d, and then the top in its row must be d. So at least one of the two tops is d, and any cell that sees both tops loses d.

A skyscraper is a skewed X-Wing: if the tops lined up as well, you would have an X-Wing.

How to spot it

  • Find the rows (columns) with only two places for d, then pair up two rows that have one end in the same column.

Common mistakes

  • Eliminating from cells that see the two bases instead of the two tops.

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Related techniques

References

The examples on this page are generated from random puzzles, not taken from these sources.