The skyscraper in sudoku
The skyscraper is the friendliest of the expert patterns, and the first built openly from strong links. A strong link is a unit where one digit has exactly two homes, so one of the two must be true. Take two strong links for the same digit in two parallel columns, stand them on a shared row, and the tops of the towers do the eliminating.
The pattern
Follow the 2s. The left marked column holds its 2 in exactly two cells, and so does the right one. The two lower cells share a row, the towers’ shared street, and the two upper cells sit at different heights, the roofs:
Both columns play fair. Run your eye down either one: placed digits fill six cells, the bottom cell shows pencil marks without a 2, courtesy of the placed 2 it can see, and exactly two candidates remain.
Why the elimination works
The two lower link ends share a row, so they cannot both be 2. At least one column must place its 2 at the top instead. You never learn which, and it never matters: in every possible world, one roof or the other is a 2. A cell that sees both roofs is looking at a 2 in every future, and its own 2 candidate is dead:
Check each struck cell against the roofs. One sits in the taller roof’s row and the shorter roof’s box. Two sit in the shorter roof’s row and the taller roof’s box. Every one of them watches both futures, and three eliminations from two strong links is a healthy trade.
How to hunt
Count homes, digit by digit, column by column: you are shopping for exactly two. Note each strong link you find, and check pairs of them for a shared end line. The roofs must also land in the same band of the board, close enough for rows and boxes to connect them to common cells; towers too far apart overlook nobody. Selecting the digit lights every candidate, and Auto notes keeps the two-home counts honest.
Near misses
The strong links carry everything, and a strong link dies the moment a third home appears:
With three homes in the left column, the shared row argument collapses: both lower cells could be innocent, and no roof is guaranteed. Verify both counts before erasing anything. Exactly two per column, no charity.
Where it fits
The skyscraper shares the expert rung with the XY-wing, the swordfish and coloring. It relaxes the X-wing’s strict rectangle by one corner, which makes it more common in the wild, and it is the gentlest introduction to strong-link thinking, the current that runs through everything above it on the ladder.
Frequently asked questions
What is a skyscraper in sudoku?
Two strong links for one digit in two parallel columns, with one end of each link sharing a row. The shared ends cannot both be true, so at least one far end is, and any cell that sees both far ends loses the digit. Swap rows and columns and the pattern works the same way.
What is a strong link?
A unit where a digit has exactly two possible cells, so one of the two must be true. Strong links are the raw material of the expert tier: skyscrapers use two of them, coloring chains many, and finding them is a counting exercise you already know from hidden singles.
Why is it called a skyscraper?
Picture the two columns as towers standing on a shared street, the base row. The towers rise to different heights, and the two roofs are where the logic pays out. The name describes the drawing more than the logic, and it stuck because the shape is easy to recognize.
Is a skyscraper related to the X-wing?
Closely. An X-wing demands that both ends of both links align in rows. The skyscraper relaxes one alignment: the bases share a row and the roofs do not. It trades the X-wing symmetry for looser geometry, and stalls that hold no X-wing often hold one of these.