專家 Kropki 數獨
黑點表示倍數關係；白點表示連續數字。未標記的對同樣攜帶強大的信息。免費在線。
專家 Kropki數獨。網站上最難的點約束謎題——每一步都鏈接點邏輯、無點刪除和高級數獨技巧。無需猜測。
4
8
1
9
2
3
7
5
7
9
4
6
5
8
4
3
6
1
7
5
6
8
2
什麼是 Kropki數獨？
難度
★★★☆☆
3/5
約束類型
單元格關係
典型給定數字
18–24
平均解題（專家）
62 分鐘
解謎技巧（專家 等級）
| 技巧 | 描述 | 等級 |
|---|---|---|
| White Dot Pairs | White dots mark consecutive digit pairs: (1,2), (2,3), …, (8,9). Cross-reference with row and column constraints. | 初學者 |
| Black Dot Pairs | Black dots mark double-relationship pairs: (1,2), (2,4), (3,6), (4,8). Only these four combinations are valid. | 初學者 |
| Negative Constraint | No dot between two cells means they are neither consecutive nor in a 1:2 ratio — a powerful elimination on every unmarked adjacent pair. | 中級 |
| Dot Chain Analysis | A sequence of connected dots forms a digit-value chain. Enumerate valid digit sequences for the entire chain simultaneously. | 進階 |
| 1-2-4 and 2-4-8 Chains | A black dot adjacent to a white dot often forces the common 1→2→4 or 2→4→8 chain. | 中級 |
在 專家 需要掌握的技巧
- X翼技巧 — Expert Kropki grids stretch dot chains until pure dot logic stalls — at that point the negative constraint has thinned 5, 7, and 9 enough for clean X-Wing rectangles.
- Swordfish technique — The 1-2-4-8 doubling skeleton confines even digits to repeating column patterns; expert endgames often resolve with a Swordfish on 4 or 8 across three dot-heavy rows.
按難度劃分的平均解題時間
簡單
8 分鐘
中等
18 分鐘
困難
35 分鐘
專家
62 分鐘
想要規則、策略和解題步驟的完整解說？
如何遊玩 Kropki數獨 →
相關變體
XV數獨
Both mark adjacent-cell relationships with a powerful negative rule — XV's sum markers play exactly like kropki's dots.
連續數獨
Isolates the white-dot half of kropki: bars mark consecutive neighbours and silence means never consecutive.
大於數獨
Adjacent-cell relationships again, but as inequalities — order information instead of difference and ratio.
常見問題 — 專家 克羅普基數獨
更多問題？請參閱完整 Kropki數獨指南.