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

Techniques to Master at Medium

  • Hidden Singles technique — Shaft cells lean low and circles lean high, polarising each crossing unit — scan rows pierced by arrows and the big digits' hidden singles fall out of the off-arrow cells.
  • Obvious Pairs technique — Short shafts reduced to {1,2} or {1,3} are instant pairs for their row and box; medium arrow puzzles chain three or four such pairs in sequence.

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 →

Related Variants

Thermo Sudoku

Arrows demand sums along a line; thermometers demand growth along one — both reward tracking minimums and maximums cell by cell.

Killer Sudoku

The cage-based cousin of arrow arithmetic, adding a no-repeat rule and the powerful 45 trick to your sum toolkit.

Renban Sudoku

Trades arithmetic for set logic on the same drawn-line canvas: line digits must form a consecutive run.

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.