Arrow Sudoku
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
Can digits repeat on an arrow?
Yes — arrow shaft cells can repeat. For example, a circle of 6 could have shaft cells (3, 3) or (1, 2, 3).
Does the circle count in the sum?
No — only the cells along the shaft count. The circle is the target sum.
Can arrows cross each other?
Yes — a crossing cell counts toward both arrows' sums.