如何玩箭头数独
Arrow 上的 Digits 必须求和为 circle 中的 digit
Arrow Sudoku is the variant that turned modern setters into minor celebrities: it is everywhere on Cracking the Cryptic, and for good reason. The rule fits in a breath — digits along an arrow's shaft sum to the digit in its circle — yet it generates some of the most elegant logic in all of Sudoku. The circle is a built-in ceiling: it can hold at most 9, so a three-cell shaft averages 3 at most, and long shafts are forced into tiny digits before you've placed anything. Unlike killer cages, shaft digits may repeat when rows, columns, and boxes allow it, which keeps you honest — you can never outsource the thinking to a combination chart. Arrow suits solvers who enjoyed killer's arithmetic but want it threaded through the grid geometrically, and puzzle fans who like openings that feel like proofs rather than scans. Expect easy arrows to play like medium classics and expert arrows to be genuine afternoon projects.
规则
标准数独规则适用： 填充每一行、每一列和每个 3×3 宫格，数字 1-9 各出现一次。
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。
关于这个谜题的来源、它如何与相关变体比较以及策略摘要，请参阅我们的 箭头数独 变体概述.
一览
如何解箭头数独
示例：打开一个箭头数独谜题
Say a three-cell arrow curls inside one box, its circle at r1c3 and shaft on r2c2, r2c3, r3c2. The shaft's minimum is 1+2+3 = 6 — three different digits in one box can't do better — so the circle is 6, 7, 8, or 9. Now suppose column 3 already contains 8 and 9. The circle drops to {6,7}. Try 6: the shaft must be exactly {1,2,3} in some order. Try 7: the shaft is {1,2,4}. Either way, the shaft cells contain 1 and 2 — so 1 and 2 are barred from every other cell of that box, and any box cell that held only {1,2} as candidates is now impossible, forcing earlier decisions elsewhere. Next, check the box's remaining digits: whichever of 3 and 4 the shaft doesn't use must sit in the box's non-arrow cells, and if only one such cell can take it, the circle resolves backwards — a 4 forced outside the shaft means the shaft is {1,2,3} and the circle is 6. This is arrow solving in miniature: bound the circle from below by the shaft's minimum, from above by its houses, then let the shared digits of every surviving combination do the eliminating.
箭头数独中的常见错误
| 错误 | 如何修复 |
|---|---|
| Assuming shaft digits can't repeat, as in killer cages | Arrow shafts may repeat digits whenever the shaft cells share no house. A two-cell shaft spanning two boxes in different rows and columns can legally be {3,3} under a 6 — prune combinations with Sudoku rules, not cage rules. |
| Ignoring the shaft's minimum sum | An n-cell shaft within one house sums to at least 1+2+…+n. Three cells means the circle is at least 6; four cells, at least 10 — impossible, unless repeats across houses lower the floor. Apply the floor before anything else. |
| Solving each arrow in isolation | The power move is intersecting arrow combinations with house logic: digits common to all surviving shaft combinations are locked into the shaft, and digits impossible in every combination are locked out. Arrows are elimination engines, not side quests. |
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.