Skyscrapers

Expert Skyscrapers is the sparsest pure-deduction tier: a 7×7 grid stripped down to the fewest clues that still force a single answer. No given cells, many blank border positions, and no what-if needed — but every remaining clue has to carry its weight. A single clue rarely forces a placement on its own at this density.

The main technique is simultaneous clue analysis: combine constraints from three or four clues that share cells to eliminate impossible values. If a top clue restricts a cell to {5, 6, 7} and a crossing left clue restricts it to {3, 5, 7}, only 5 or 7 survive. Enumerate the arrangements each clued line allows and intersect them with the Latin-square constraints. Pencil marks are essential for tracking these intersections.

When a candidate set reduces to one value, place it and propagate the elimination through its row and column. Expert puzzles often have a critical “unlock” point where several chains converge and a burst of placements follows. Every board is uniquely solvable by deduction alone — no guessing — but it will test your patience. When you are ready for boards that demand contradiction reasoning, try Einstein.