Arrow Sudoku
9
2
6
8
3
8
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6
1
5
7
6
3
1
9
7
8
3
5
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5
1
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6
9
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1
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9
5
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9
8
How to play Arrow Sudoku
Standard Sudoku rules apply. Extra rule: the digits along each arrow's tail must sum to the digit in the circle at the arrow's base. The circle itself is a normal Sudoku cell — its value determines what the arrow cells must sum to.
Full guide →
Digits on an arrow must sum to the digit in the circle
What is Arrow Sudoku?
Arrow Sudoku places arrows on the grid, each starting from a circled cell. The digits in all cells along the arrow (not including the circle) must sum to the digit placed in the circled cell. Since the maximum digit is 9, long arrows with many cells are highly constrained. Arrow Sudoku often combines beautifully with standard elimination and candidate logic.
At a Glance
| Constraint type | Line Constraints |
| Typical givens | 20–26 |
| Difficulty rating | ★★★★☆ 4/5 |
| Avg. solve time — Easy | 12 min |
| Avg. solve time — Medium | 25 min |
| Avg. solve time — Hard | 50 min |
| Avg. solve time — Expert | 80 min |
How to Solve Arrow Sudoku
| Technique | What it does | Level |
|---|---|---|
| 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. | Beginner |
| 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. | Intermediate |
| 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. | Beginner |
| Arrow–Region Interaction | Arrow cells sharing a box or row with the circle create indirect constraints — combine the sum equation with standard Sudoku uniqueness. | Intermediate |
| Repeating Digits on Arrows | Arrow shaft cells can repeat digits (unlike Killer cages). Factor this in when enumerating possible sums. | Advanced |
Average Solve Times
Easy
12 min
Medium
25 min
Hard
50 min
Expert
80 min
Frequently Asked Questions
What is Arrow Sudoku?
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.