困難Kropki 數獨
黑點表示倍數關係；白點表示連續數字。未標記的對同樣提供重要資訊。免費線上遊玩。
困難 Kropki數獨。密集的點網絡和更少的給定數字——多點鏈以意想不到的方式限制整行和整宮。
5
4
9
8
2
5
6
6
3
1
1
9
8
2
7
3
1
6
9
8
4
7
6
2
4
9
1
什麼是 Kropki數獨？
難度
★★★☆☆
3/5
約束類型
儲存格關係
典型給定數
18–24
平均解題時間（困難）
35分鐘
解題技巧：困難 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 |
準備好終極測試了嗎？試試 專家 Kropki數獨 — 數獨 上最難的謎題。
在 困難 需要掌握的技巧
- Hidden Pairs technique — Chains of dots (black–white runs like 2-4-5) consume candidates along their length; recount the crossing boxes afterwards, because hard Kropki pairs hide where chains intersect units.
- X-Wing 技巧 — Digit 9 joins only one white-dot pair (8,9) and no black-dot pair, so dots and their absence rapidly pin 9's legal cells — fish on 9 first in hard Kropki.
依難度平均解題時間
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演練嗎？
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 — 困難 克羅普基數獨
還有問題？請參閱完整 Kropki數獨指南.