箭头数独
5
6
7
9
4
6
7
1
2
5
7
5
4
3
7
8
1
4
4
5
8
3
2
6
2
8
5
7
2
5
1
4
3
7
8
9
5
6
Arrow 上的 Digits 必须求和为 circle 中的 digit
什么是箭头数独？
Arrow Sudoku 在网格上放置箭头，每个箭头从一个带圆圈的单元格开始。箭头沿途所有单元格（不包括圆圈）中的数字之和必须等于圆圈单元格中的数字。由于最大数字是9，长箭头（包含多个单元格）受到高度限制。Arrow Sudoku 通常与标准排除法和候选数逻辑完美结合。
一览
| 约束类型 | 线条约束 |
| 典型给定数 | 20–26 |
| 难度评级 | ★★★★☆ 4/5 |
| 平均解题时间 — 简单 | 12 分钟 |
| 平均解题时间 — 中等 | 25 分钟 |
| 平均解题时间 — 困难 | 50 分钟 |
| 平均解题时间 — 专家 | 80 分钟 |
如何解箭头数独
| 技巧 | 它的作用 | 级别 |
|---|---|---|
| Arrow Sum Bounding | The circle digit equals the sum of all arrow shaft cells. A 3-cell arrow with circle 5 means the three shaft cells average under 2 — severely constraining options. | 高级 |
| Max/Min Arrow Analysis | The maximum sum of N cells is 9+8+7+…; the minimum is 1+2+3+…. If the circle digit falls outside these bounds, a constraint error exists. | 高级 |
| Bifurcation on Short Arrows | For 2-cell arrows with a small circle (e.g., 3), only (1,2) or (2,1) works — enumerate cases to find forced placements quickly. | 高级 |
| Arrow–Region Interaction | Arrow cells sharing a box or row with the circle create indirect constraints — combine the sum equation with standard Sudoku uniqueness. | 高级 |
| Repeating Digits on Arrows | Arrow shaft cells can repeat digits (unlike Killer cages). Factor this in when enumerating possible sums. | 高级 |
平均解题时间
简单
12 分钟
中等
25 分钟
困难
50 分钟
专家
80 分钟
常见问题
什么是箭头数独？
Arrow Sudoku is a variant where arrows are drawn across the grid. Every digit placed along an arrow must sum to the number written inside the circle at the arrow's base. Standard Sudoku rules still apply — every row, column, and 3×3 box must contain the digits 1–9 exactly once.
How do the arrows and circles work?
Each arrow starts at a circle and extends through one or more cells. The digit in the circle is the target sum for all cells the arrow passes through. A single-cell arrow tells you the exact digit in that cell. Longer arrows have multiple possible combinations, which you narrow down using Sudoku constraints.
Is Arrow Sudoku harder than regular Sudoku?
It depends on your experience. Arrow Sudoku adds an arithmetic layer on top of standard logic. Easy puzzles are comparable in difficulty to medium classic Sudoku. Hard and expert arrow puzzles require simultaneous constraint-tracking that most players find significantly more challenging than any classic Sudoku difficulty.
Can a digit repeat along an arrow?
No — digits can repeat on an arrow only if standard Sudoku rules allow it. Because each row, column, and box must contain 1–9 once, a digit can appear twice on an arrow only if the two cells are in different rows, columns, and boxes. In practice, most arrow cells are highly constrained.
What is the best first move in Arrow Sudoku?
Start with single-cell arrows — the digit in that cell equals the circle value directly. Then look for short arrows with extreme sums. A 2-cell arrow summing to 3 can only be {1,2}; summing to 17 can only be {8,9}. These give you the tightest starting constraints without any guessing.
How long does Arrow Sudoku take to solve?
Easy puzzles take 5–15 minutes. Medium puzzles typically run 15–30 minutes. Hard puzzles average 30–60 minutes, and expert puzzles can take over an hour even for experienced solvers. Solve times improve quickly once you develop intuition for which arrow combinations are possible at a glance.