困难 黑白点数独
黑点表示倍数关系；白点表示连续数字。未标记的数对携带同样强大的信息。免费在线玩。
困难 黑白点数独。密集的点网络和更少的已知数——多点链以意想不到的方式限制整行和整宫。
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
什么是黑白点数独？
难度
★★★☆☆
3/5
约束类型
单元格关系
典型给定数
18–24
平均解题 (困难)
35 分钟
困难 级别的解题技巧
| 技巧 | 描述 | 级别 |
|---|---|---|
| White Dot Pairs | White dots mark consecutive digit pairs: (1,2), (2,3), …, (8,9). Cross-reference with row and column constraints. | 初级 |
| Black Dot Pairs | Black dots mark double-relationship pairs: (1,2), (2,4), (3,6), (4,8). Only these four combinations are valid. | 初级 |
| 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. | 中级 |
| Dot Chain Analysis | A sequence of connected dots forms a digit-value chain. Enumerate valid digit sequences for the entire chain simultaneously. | 高级 |
| 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. | 中级 |
准备好终极测试了吗?试试 专家 黑白点数独 — 数独 上最难的谜题。
在困难需要掌握的技巧
- 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翼技巧 — 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.
按难度划分的平均解题时间
简单
8 分钟
中等
18 分钟
困难
35 分钟
专家
62 分钟
想要规则、策略和解题步骤的完整指南吗？
如何玩黑白点数独 →
相关变体
XV数独
Both mark adjacent-cell relationships with a powerful negative rule — XV's sum markers play exactly like kropki's dots.
连续数独
Isolates the white-dot half of kropki: bars mark consecutive neighbours and silence means never consecutive.
大于数独
Adjacent-cell relationships again, but as inequalities — order information instead of difference and ratio.
常见问题 — 困难 黑白点数独
更多问题？请参阅完整 黑白点数独指南.