Skyscrapers

Each cell holds a building 1..n tall, once per row and column; the numbers outside say how many buildings are visible from that side.

What it is

A Latin square read from its edges. Looking along a line, a building is visible only if every building before it is shorter — so a clue of 1 means the tallest stands nearest, and a clue of n means the line ascends step by step. Everything between is deduction.

How to play

The extremes go in first (1 and n force whole lines). After that, work out which arrangements of a line are still consistent with what you know and its clue: heights that appear in none of them are impossible.

Why it is in the catalogue

The third one value per cell puzzle on the shared engine, after ripple and futoshiki: rows and columns are AllDifferent, uniqueness and thinning are the shared routines, the rating is the technique ladder. The only new code is the visibility clue.

History

A Japanese puzzle-magazine staple (also Building, Towers, Wolkenkratzer) popularised worldwide through Croco-Puzzle and the World Puzzle Championship, where it is a regular round.

The implementation’s guarantees

• The clue rule is a line solver, not rules of thumb. The first version implemented the three deductions a person names first (clue 1 forces the tallest, clue n forces the ascent, height caps by position) and the ladder could not finish a single board: those prune the extremes and say almost nothing about the middle clues, which are most of a page. The propagator now enumerates the arrangements still consistent with the domains and eliminates heights absent from all of them — affordable because a line is at most 7 cells, pruned by domains and by running visibility.
• It sits on the ladder at SumCombination, the rung kakuro’s combination reasoning uses, and for the same reason: one clue’s own bookkeeping, no cross-referencing.
• Uniqueness and no guessing are proved on the board that ships, and the answer is checked against the rules directly (obeys) before any search.
• Clues are thinned while the ladder can still finish unaided — the shipped 5×5 typically prints 8–10 of the 20 possible.
• Rating basis: technique_ladder.