THE SETUP — TWO RULES TO HOLD
- Latin square: every digit 1–N appears exactly once per row and column.
- Visibility: the edge clue tells you how many buildings are visible from that side. A taller building hides all shorter buildings behind it.
On a 5×5 grid the digits are 1–5. The edge clues range from 1 to 5. Apply the visibility clues first — they locate the 5 — then use Latin-square elimination to fill the rest.
TECHNIQUE 1 — CLUE 1: TALLEST BUILDING AT THE EDGE
A clue of 1 means only one building is visible. That is only possible if the tallest building (N) is right at the edge — it immediately blocks everything behind it.
Action: whenever you see a clue of 1, the cell nearest to it in that row or column is N. Place it immediately. This is the fastest single-clue deduction in the puzzle.
TECHNIQUE 2 — CLUE N: THE FULL ASCENDING SEQUENCE
A clue equal to N (the maximum, e.g. 5 on a 5×5 grid) means every building is visible. That is only possible if the buildings increase from the edge inward: 1, 2, 3, 4, 5 in exact order.
Action: whenever you see a clue of N, fill the entire row or column in ascending order from the clue side. No further logic needed — the row is done.
On a 5×5 puzzle, two or three clue-1 and clue-5 entries often resolve a third of the grid before you think about any other technique.
TECHNIQUE 3 — LOCATING N IN EVERY ROW AND COLUMN
After clue-1 and clue-N are applied, locate N in every remaining row and column by cross-referencing the two clues on opposite ends.
A clue of k on one side means N is not in the first k−1 positions from that side (otherwise you'd see fewer than k buildings). So from that direction, N must be at position k or later. Apply the same logic from the opposite clue. The overlap of both ranges tells you exactly which cells N can occupy.
Row with clue 3 on the left, clue 2 on the right (5×5):
From left: N not in positions 1 or 2 → N at positions 3, 4, or 5
From right: N not in position 1 (rightmost) → N at positions 1–4 from the left
Intersection: N must be at position 3 or 4.
When the intersection is a single position, N is placed. When it's two or three positions, pencil-mark them and move to other rows to narrow further.
TECHNIQUE 4 — LATIN-SQUARE SWEEP AFTER PLACING Ns
Once you've placed N in most rows and columns, switch to Latin-square elimination. N appears exactly once per row and once per column — so any row or column that already has N eliminates it from all other cells in that line.
This cross-elimination usually forces N into the remaining cells faster than reworking the visibility clues. Alternate between visibility-range checks and Latin-square sweeps until all cells are filled.
THE SOLVING ORDER
- Apply all clue-1 entries. Place N in those edge cells.
- Apply all clue-N entries. Fill those rows/columns completely (ascending sequence).
- For every remaining row and column: compute the range for N using both opposing clues. Place N where it's forced.
- Use Latin-square elimination to narrow N into any still-unknown positions.
- Once all Ns are placed: fill smaller digits using Latin-square elimination + visibility counting (how many buildings are already visible in each partially-filled row/column).
Steps 1–4 alone usually place N in every row and column. After that the puzzle reduces to a Latin square with several cells already known.
THE BEGINNER TRAP
Filling the Latin square first without using the visibility clues. If you start by placing digits 1 through N-1 via elimination alone, you discard most of what the edge clues tell you. The clues constrain the tallest building's position — which is the most powerful constraint — and ignoring them forces you to guess on every intermediate row.
Always place N first, using the visibility clues. N is the master key: every other digit in a row or column is placed in relation to where N sits.