Hard 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

Hard Arrow Sudoku. Long arrows with many possible combinations require full enumeration and careful cross-referencing with standard Sudoku constraints.

5
1
7
3
6
8
7
2
6
2
7
1
8
9
9
3
1
2
1
6
3
1
8
9
3
4
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 (Hard)
50 min

Solving Techniques for Hard 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

Ready for the ultimate test? Try Expert Arrow Sudoku — the hardest puzzles on Sudoku.by.

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 — Hard Arrow Sudoku

What makes hard Arrow Sudoku difficult?
Hard Arrow Sudoku has long arrows with many possible tail combinations, and the circle values are harder to determine without first partially resolving the tails. You must work simultaneously on arithmetic constraints and standard Sudoku logic, often cycling between the two multiple times before any digit is placed.
How do I handle a long arrow tail with many combinations?
For a tail of 4+ cells, enumerate all combinations that sum to the circle's possible range of values (since the circle may not be known yet). Then eliminate combinations that require a digit already placed in the same row, column, or box. The remaining combinations often share a common digit in a specific position, which is a forced placement.
What is a forced circle digit in Arrow Sudoku?
A forced circle digit occurs when, regardless of which valid combination fills the arrow tail, the circle must hold the same value. This happens when all tail combinations that satisfy row, column, and box constraints produce the same sum. Spotting forced circles is a key deduction technique at hard level.
Should I use pencil marks for hard Arrow Sudoku?
Yes — pencil marks are essential. Track candidate digits for every cell, including both arrow tails and circles. As you narrow down tail combinations, update the candidates for each tail cell. Without a complete candidate grid, multi-arrow interactions are nearly impossible to track.
How long does a hard Arrow Sudoku take?
Expect 35–60 minutes for hard Arrow Sudoku. Experienced solvers who routinely enumerate arrow combinations can finish in 25–40 minutes.

More questions? See the full Arrow Sudoku guide.