Skyscrapers techniques

Naked Single

Only one candidate height remains for this cell — place it.

Hidden Single

A height has only one possible cell left in this row or column, even though that cell has other candidates too.

Clue of One

A clue of 1 means the tallest building is visible right at that edge — place the max height there.

Full Visibility Clue

A clue equal to the grid size means every building is taller than the last — the whole line is forced into one exact order.

Visible-Count Bound

A clue of k means the tallest building can't sit within the first k-1 cells from that edge — eliminate it there.

Line Consistency

Every way to fill this row or column's remaining heights that matches its clue was checked — a height eliminated here doesn't appear in any of them.

Naked Pair

Two cells in a row or column share the exact same two candidate heights — remove those heights from the rest of the line.

Hidden Pair

Two heights only fit in the same two cells of a row or column — strip those cells down to just those two.

Naked Triple

Three cells in a row or column whose candidates combine to exactly three heights — eliminate those heights elsewhere in the line.

Hidden Triple

Three heights only fit in the same three cells of a row or column — strip those cells down to just those three.

X-Wing

A height's only two candidate cells line up in the same two columns (or rows) across two rows (or columns) — eliminate it everywhere else in those columns or rows.

Naked Quad

Four cells in a row or column whose candidates combine to exactly four heights — eliminate those heights elsewhere in the line.

Hidden Quad

Four heights only fit in the same four cells of a row or column — strip those cells down to just those four.

This row or column has only a few arrangements left that match its clue — any one that leaves some other row or column with no way to finish is out, and a height used by none of the survivors can be struck.

XY-Wing

A cell with two candidates links to two other two-candidate cells that share one candidate each with it and one with each other — the shared height can't be in any cell both of those see.

W-Wing

Two cells share the same candidate pair and aren't in the same row or column, but a chain elsewhere forces one of them to one of those heights — eliminate the other height from any cell both see.

XYZ-Wing

A three-candidate cell links to two two-candidate cells whose combined candidates match it exactly — the shared height can't be in any cell all three see.

Swordfish

A height's candidate cells across three rows (or columns) line up in the same three columns (or rows) — eliminate it everywhere else in those columns or rows.

Jellyfish

A height's candidate cells across four rows (or columns) line up in the same four columns (or rows) — eliminate it everywhere else in those columns or rows.

Cross-Line Forcing

Same as Cross-Line Consistency, but each arrangement is also followed through: fill in every height it forces outright, and rule it out if that leaves some other row or column unfinishable.

Contradiction

Placing this height in this cell forces some row or column to have no valid arrangement left — so that height can be ruled out here.