Skyscraper數獨
3
5
3
1
4
2
3
2
2
2
3
1
2
3
2
3
3
3
5
1
3
9
8
7
7
2
5
6
7
3
4
5
1
8
7
4
2
6
9
3
8
7
9
5
4
6
7
4
8
5
2
4
3
1
8
5
5
1
5
2
4
2
3
2
3
4
3
2
4
4
2
1
2
4
外部提示顯示從該邊界可以看到多少個「建築物」
什麼是 Skyscraper數獨？
摩天大樓數獨將每個數字想像成該高度的建築物。網格外部的提示表示從該邊緣向內看可以看到多少棟建築物——較高的建築物會遮擋所有較矮的建築物。提示為1表示第一棟建築物必須是9。提示為9表示建築物按嚴格遞增順序排列（1,2,3,4,5,6,7,8,9）。此變體需要同時運用數獨邏輯和排列推理。
一覽
| 約束類型 | 外部線索 |
| 典型給定數 | 4–10 clue values |
| 難度評分 | ★★★★☆ 4/5 |
| 平均解題時間 — 簡單 | 12分鐘 |
| 平均解題時間 — 中等 | 25分鐘 |
| 平均解題時間 — 困難 | 50分鐘 |
| 平均解題時間 — 專家 | 80分鐘 |
如何解 Skyscraper數獨
| 技巧 | 它的作用 | 等級 |
|---|---|---|
| Clue 1 Forces 9 First | A visibility clue of 1 means the first building from that edge must be a 9. All shorter buildings behind it are hidden. | 進階 |
| Clue 9 Forces Ascending Order | A clue of 9 means all buildings are visible, so digits are in strictly ascending order from that edge: 1, 2, 3, 4, 5, 6, 7, 8, 9. | 進階 |
| Permutation Enumeration | For each clue value V, enumerate all permutations of 1–9 that give exactly V visible buildings. Cross-reference opposite-edge clues. | 進階 |
| 9 Always Visible | The digit 9 is always visible from either edge. The digit 8 is visible only if it appears before any 9 from that edge. | 進階 |
| Multi-Edge Constraint | Combine the clue from one edge with the opposite edge's clue. Both must be simultaneously satisfiable. | 進階 |
平均解題時間
簡單
12分鐘
中等
25分鐘
困難
50分鐘
專家
80分鐘
常見問題
什麼是 Skyscraper Sudoku？
Skyscraper Sudoku is a variant where numbers appear outside the grid on all four sides. Each number tells you how many distinct 'buildings' (digits) are visible when looking into that row or column from that side. Taller buildings hide shorter ones behind them — a larger digit blocks any smaller digit placed further into the row.
How does visibility work in Skyscraper Sudoku?
Imagine the digits in a row as buildings of different heights. Looking from one end, you can see a building only if no taller building stands between you and it. A clue of 1 means only the first building is visible, so it must be the tallest (digit 9). A clue of 9 means all buildings are visible, so the row must be in ascending order from that side.
What do extreme clue values tell me?
A clue of 1 means the first cell from that side holds a 9 — it blocks everything else. A clue of 9 means the row or column is in strictly ascending order from that direction (1,2,3,4,5,6,7,8,9). Both are immediately actionable. Mid-range clues require enumerating valid permutations.
Is Skyscraper Sudoku harder than regular Sudoku?
Yes, generally. Skyscraper clues require enumerating valid digit permutations for each row and column, which is more combinatorially intensive than classic Sudoku elimination. Easy puzzles are accessible; hard and expert puzzles require tracking visibility across multiple rows and columns simultaneously.
What is the best first strategy for Skyscraper Sudoku?
Start with clues of 1 and 9 — they immediately fix a digit or fully determine the order of a row. Then look for clues of 2, which constrain the position of the 9 significantly. Combine skyscraper deductions with standard Sudoku box and row/column scans.
How long does Skyscraper Sudoku take to solve?
Easy puzzles take 8–20 minutes. Medium puzzles run 20–40 minutes. Hard puzzles average 40–75 minutes and expert puzzles often exceed 90 minutes. Fast solvers develop the ability to enumerate valid visibility permutations quickly without writing them all out.