Arrow Sudoku is a Sudoku variant — a sum sudoku where some cells contain circles with arrows running through the grid. Standard Sudoku rules apply, with one extra constraint: the digits along each arrow must add up to the digit in the circled cell at the arrow's base. Digits may repeat along an arrow unless other Sudoku rules forbid it. This arithmetic twist is what makes it one of the most approachable variant sudokus for newcomers.
The Rules of Arrow Sudoku
Every Arrow Sudoku starts from the familiar 9×9 grid:
- Standard Sudoku rules apply. Place the digits 1–9 so that no digit repeats in any row, column, or 3×3 box.
- The arrow sum rule. Some cells contain a circle (sometimes called the "pill") with an arrow extending through neighbouring cells. The digits placed along the arrow's path must sum to the digit in the circled cell.
- Repeats are allowed on arrows. Unlike rows and columns, digits may repeat along a single arrow — the only requirement is that they add to the circle's total. (Standard Sudoku rules still ban repeats in the same row, column, or box.)
- The circle is part of the grid. The circled cell is a normal cell too: it must obey row, column and box rules as well as being the arrow's total.
A concrete example from a PuzzleMadness walkthrough (puzzlemadness.co.uk): if a circle needs a total of 9 and one cell on its arrow already holds a 6, the other cell on that arrow must be 3. This kind of simple arithmetic is the heart of the variant.
What the arrows look like
Arrows can be short (two or three cells) or snake across the grid. The circle always sits at the "base" — the digits on the arrow's shaft add up to it. Some puzzles combine arrows with other variant rules (thermometers, killer cages), but pure Arrow Sudoku uses only the sum constraint.
Why Arrow Sudoku Is So Popular
Arrow Sudoku owes much of its fame to the variant-Sudoku boom led by the YouTube channel Cracking the Cryptic, whose hosts Simon Anthony and Mark Goodliffe regularly feature arrow puzzles — including constructions by Dutch grandmaster Aad van de Wetering — to audiences of hundreds of thousands. The variant also appears in competitive solving: hybrid rounds at events like the World Sudoku Championship have mixed arrows with thermometers.
Its appeal is easy to see:
- Arithmetic meets logic. You get the satisfaction of Sudoku's pure deduction plus the number-crunching of sums.
- Low givens, high logic. Arrow puzzles often start with very few given digits, yet remain fully logical — the arrows carry the information.
- Gentle learning curve. The sum rule is intuitive; anyone who can add can start solving.
Strategies and Tips for Arrow Sudoku
Arrow cells behave differently from normal cells, and the best solvers exploit that:
- Start with the total cells. Circles are usually large digits (arrows need room to add up), so they eliminate small candidates immediately. A circle that must total at least 10 can't be 1–9's small end — begin there.
- Bound the possibilities. A two-cell arrow totalling 9 can only be (1,8), (2,7), (3,6) or (4,5) in some order — and Sudoku's row/column rules cut that list fast.
- Watch for short arrows. A single-cell arrow simply copies the circle's digit into the adjacent cell — free information.
- Use the 45 rule. Each row, column and box sums to 45 (1+2+…+9). Comparing arrow totals against 45 reveals hidden constraints, especially where arrows cross unit boundaries.
- Combine with standard techniques. Hidden singles, pairs, and pointing pairs work exactly as in classic Sudoku — apply them to shrink arrow possibilities.
- Don't forget repeats are legal. Newcomers often wrongly assume arrow digits must differ. They don't; only the sum matters.
Arrow Sudoku vs Other Sudoku Variants
| Variant | Extra rule | Difficulty feel |
|---|---|---|
| Classic Sudoku | None | Baseline |
| Arrow Sudoku | Arrow digits sum to the circled digit | Medium — arithmetic adds a layer |
| Killer Sudoku | Digits in dashed cages sum to the cage total, no repeats in a cage | Medium-hard |
| Thermo Sudoku | Digits strictly increase along thermometers from bulb to tip | Medium |
| Thermo-Arrow hybrid | Both thermometer and arrow rules apply | Hard |
Arrow Sudoku is often recommended as the friendliest "first variant" because its single extra rule is so easy to grasp. If you're ready for a tougher sum-based challenge afterwards, try our killer sudoku guide.
Where to Play Arrow Sudoku Online
- PuzzleMadness (puzzlemadness.co.uk) — free daily Arrow Sudoku in Easy, Medium, Hard, Tough and Mixed difficulties, with guided starting hints.
- GMPuzzles / The Art of Puzzles (gmpuzzles.com) — hand-crafted Arrow Sudoku from the Genuinely Approachable Sudoku (GAS) series, including beginner-friendly "easiest" collections, solvable online via SudokuPad.
- SudokuPad (sudokupad.app) — the community's favourite interface for playing and sharing variant puzzles, used by setters and streamers alike.
- Cracking the Cryptic (crackingthecryptic.com) — apps and puzzle packs featuring arrow puzzles from top constructors.
- Fun With Puzzles (funwithpuzzles.com) — long-running blog series including hybrid Thermo-Arrow puzzles with published solutions.
For more daily puzzles, browse our daily puzzle games list.
The Bottom Line
Arrow Sudoku takes the world's favourite number puzzle and adds one elegant twist: make the arrows add up. Learn the sum rule, start with the circle cells, and use the 45 rule when things get tight — then try a daily puzzle on PuzzleMadness or a hand-crafted grid from GMPuzzles to put your new skills to work. Once the arrow sums feel natural, the same deduction habits carry over to killer sudoku and thermo sudoku — and those variant skills feed right back into faster classic solving, because arithmetic puzzles train the candidate-tracking muscles that pure-logic grids rely on.
Arrow Sudoku Arithmetic Shortcuts
Arrow puzzles look like pure logic, but speed comes from arithmetic fluency — knowing the possible sums instantly rather than working them out. Here are the shortcuts that matter.
Memorise the small-circle partitions. Short arrows are the puzzle's givens in disguise. A circle totalling 3 with a two-cell arrow can only be (1,2). A circle of 4 with two cells is (1,3) — never (2,2), because repeats are banned only where sudoku rules forbid them, and a two-cell arrow in the same row cannot repeat anyway. Learn the two-cell partitions for totals 3 through 10 cold; they appear constantly.
Use the circle as a range limiter. A circled cell showing 9 with a four-cell arrow tells you something powerful: the average arrow cell is just over 2, so the arrow must contain small digits. Conversely, a circle of 30 on a four-cell arrow forces large digits (average 7.5). Before placing anything, bracket the arrow's digits into "small", "medium", or "large" — this single habit eliminates half the candidate space.
Exploit the maximum-sum rule. An arrow of length n cannot exceed a sum achievable with distinct-where-required digits, but more usefully: if a circle shows a total that is close to the maximum possible for its arrow length, the arrow's digits are nearly forced. A three-cell arrow totalling 24 must be some arrangement of (7,8,9). Spotting near-maximum and near-minimum totals turns arithmetic into givens.
Chain arrows through shared cells. Where two arrows cross or share a cell, the shared digit must satisfy both sums simultaneously. These intersections are the puzzle's natural breakpoints — solve them first, and each arrow's remaining cells collapse quickly.
What are the rules of Arrow Sudoku?
Normal Sudoku rules apply, plus: digits along each arrow must sum to the digit in the circled cell at the arrow’s base. Digits may repeat along an arrow.
Can numbers repeat on an arrow in Arrow Sudoku?
Yes. Repeats are allowed along a single arrow as long as the digits add up to the circle’s total and don’t break row, column or box rules.
What is the circle in Arrow Sudoku?
The circle (or “pill”) is the cell at the base of an arrow. Its digit must equal the sum of all digits along that arrow’s path.
Is Arrow Sudoku harder than normal Sudoku?
Slightly — the arithmetic adds a layer of reasoning, but the single extra rule makes it one of the easiest Sudoku variants to learn.
Where can I play Arrow Sudoku for free?
PuzzleMadness offers a free daily Arrow Sudoku with five difficulty levels, and GMPuzzles hosts free hand-crafted puzzles playable in SudokuPad.
What’s the difference between Arrow Sudoku and Killer Sudoku?
Both use sums, but Killer Sudoku’s cages forbid repeating digits within a cage, while Arrow Sudoku allows repeats along arrows. Killer cages can also span irregular shapes; arrows follow a fixed path to a circle.
What is the smallest possible arrow total in Arrow Sudoku?
A two-cell arrow has a minimum total of 3 (1+2). In general, the minimum sum for an n-cell arrow is 1+2+…+n — though remember that digits may repeat along an arrow unless row, column, or box rules forbid it, so the true minimum depends on the arrow’s position.
Do arrow totals include the circled cell itself?
No — the circled cell holds the *target* total, and only the digits along the arrow’s shaft add up to it. The circle is also a normal grid cell that must satisfy row, column, and box rules, which is what makes high-total circles so constraining.