Expert 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

Expert Arrow Sudoku. Multi-arrow forcing chains and parity reasoning are required. The hardest arrow puzzles on the site — every digit is logically provable.

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

What is Arrow Sudoku?

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

Solving Techniques for Expert 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
Repeating Digits on Arrows Arrow shaft cells can repeat digits (unlike Killer cages). Factor this in when enumerating possible sums. Advanced

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 — Expert Arrow Sudoku

Is expert Arrow Sudoku solvable without guessing?
Yes. Every expert Arrow Sudoku on Sudoku.by has a unique solution reachable through pure logic. Arrow arithmetic provides enough constraint — even with sparse given digits — to resolve the puzzle without bifurcation when all arrow-sum relationships are fully exploited.
What advanced techniques are used in expert Arrow Sudoku?
Expert puzzles require multi-arrow forcing chains: sequences where fixing a digit in one arrow's circle forces the tail combination, which forces digits in other cells, which constrains other arrows. You may also need to exploit parity — whether an arrow sum is odd or even — to eliminate entire classes of combinations.
How does arrow-sum parity help at expert level?
If an arrow circle must be odd (forced by its row, column, or box), and the tail has an even number of cells, only combinations summing to an odd number are valid. This parity filter can eliminate half the possible combinations instantly, making expert puzzles tractable when the arithmetic seems overwhelming.
How many given digits does an expert Arrow Sudoku have?
Expert puzzles typically provide very few pre-filled digits — most information comes from the arrow constraints themselves. The arrows collectively provide a web of sum relationships that, when fully analyzed, uniquely determine the solution.
How long does an expert Arrow Sudoku take to solve?
Expert Arrow Sudoku puzzles take most players 60–100 minutes. If you're stuck, revisit your arrow enumeration for the longest arrows — there is almost always a combination you haven't fully eliminated, and finding it usually triggers a cascade of new deductions.

More questions? See the full Arrow Sudoku guide.