Medium Arrow Sudoku

Digits along each arrow must sum to the number in the circle. Arrows and classic Sudoku rules combine for pure logic.

Easy Medium Hard Expert

Arrow Sudoku at medium difficulty. Overlapping arrows create powerful intersections — focus on cells that appear on two or more arrows simultaneously.

2
4
6
3
5
8
4
6
3
9
7
8
9
4
6
2
8
4
7
3
4
9
8
4
6
2
5
7
9
5
1
4
Mistakes
0/3
Score
-
Time
00:00
Try Hard →
Progress0%

What is Arrow Sudoku?

Difficulty
★★★★☆
4/5
Constraint Type
Line Constraints
Typical Givens
20–26
Avg. Solve (Medium)
25 min

Solving Techniques for Medium Level

Technique Description 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

Master these, then take on Hard Arrow Sudoku to learn Advanced techniques.

Average Solve Time by Difficulty

Easy
12 min
Medium
25 min
Hard
50 min
Expert
80 min
Want a full walkthrough of rules, strategies, and solving steps? How to Play Arrow Sudoku →

Frequently Asked Questions — Medium Arrow Sudoku

What techniques help with medium Arrow Sudoku?
At medium difficulty, use arrow arithmetic combined with standard naked pairs and hidden singles. When you know the circle's digit, you can enumerate all combinations that sum to it for the tail length. Cross-referencing those combinations with row, column, and box constraints usually narrows each tail cell to one or two candidates.
How do overlapping arrows help in Arrow Sudoku?
When two arrows share a cell, that cell must simultaneously contribute to both sums. This intersection dramatically reduces the valid digit options for the shared cell. Look for overlapping arrows first — they often provide the most constrained deductions in a medium puzzle.
What is arrow-sum enumeration?
Arrow-sum enumeration means listing all digit combinations (with repetition allowed) that sum to the circle's value for the given tail length. For example, a 3-cell tail summing to 7 could be {1,2,4}, {1,3,3}, {2,2,3}. You then eliminate combinations that violate row, column, or box uniqueness.
How does knowing a circle's digit constrain the tail?
Once you determine the circle's digit, the tail becomes a constrained subset sum problem: find all ways to sum to that digit with the available tail cells. If the circle holds 5 and the tail has 2 cells, the only options are {1,4} and {2,3}. Cross-reference with existing digits in those cells' rows and columns to narrow it further.
How long does a medium Arrow Sudoku take?
Most players complete a medium Arrow Sudoku in 15–30 minutes. The time scales with how many overlapping arrows the puzzle contains — more overlaps mean more constraints and usually a faster solve.

More questions? See the full Arrow Sudoku guide.