Tower Logic — Skyscraper Height Puzzle
Place towers 1-4 so no height repeats per row/column and clues show visible towers from each edge.
How to play
- Each row and column must contain heights 1, 2, 3, and 4 with no repeats.
- The blue numbers around the border are 'visibility clues' from each edge.
- A clue of 1 means only the tallest tower (4) is visible right at the edge.
- A clue of 4 means you see towers 1, 2, 3, 4 in ascending order.
- Click a cell to select it, then press 1–4 to set its height.
Place towers of heights 1–4 in a 4x4 grid. No height may repeat in any row or column. The blue numbers around the edge show how many towers are visible when looking from that direction (taller towers hide shorter ones behind them).
How it works
Tower Logic (also called the Skyscraper puzzle) is played on a 4x4 grid. You must place towers of heights 1, 2, 3, and 4 in every row and column — each height used exactly once per row and column, like Sudoku. Numbers printed along the edges of the grid are visibility clues: they tell you exactly how many towers are visible when looking along that row or column from that edge.
A taller tower blocks any shorter tower behind it. For example, looking along a row from the left, a height sequence of 3, 1, 4, 2 reveals three towers: 3 (visible), 1 (hidden behind 3), 4 (visible), 2 (hidden behind 4).
Key deductions: a clue of 1 means the tallest tower (height 4) is nearest to you in that line. A clue equal to the grid size means towers must be arranged in ascending order from your viewpoint. Use these anchor deductions to eliminate possibilities in other lines.
Tower Logic is a precise constraint-satisfaction puzzle that exercises logical reasoning without requiring any arithmetic beyond simple comparisons.
Worked example
Using edge clues to place the tallest tower
- Find a row with a left-side clue of 1.
- A clue of 1 means only one tower is visible from the left — so the tallest tower (4) must be in the first cell of that row.
- Place 4 in cell (row, col 1).
- Now find the column containing that cell and note its top clue — the presence of 4 early in the column constrains other column placements.
- Use remaining row and column clues to fill the rest of the grid by elimination.
The tallest tower is correctly anchored, unlocking further deductions across the grid.
Common mistakes to avoid
- Forgetting that visibility is counted from the edge inward, and accidentally counting from the wrong direction.
- Placing heights correctly within a row but violating the column uniqueness constraint by duplicating a height in a column.
- Ignoring clues on the far side of a row or column — both sides contribute constraints and should be used together.
Key terms
- Visibility clue
- A number on the edge of the grid indicating how many towers can be seen looking from that edge along the adjacent row or column.
- Blocking
- When a taller tower hides all shorter towers behind it from a given viewpoint.
- Latin square constraint
- The rule that each height (1-4) appears exactly once in every row and every column, analogous to Sudoku.
Frequently asked questions
- What does the clue number mean?
- The clue tells you how many towers you can see when looking along that row or column from that edge. A tall tower hides all shorter towers behind it.
- How do I enter numbers?
- Click a cell to select it (turns blue), then press 1–4 on the keyboard.