Arrow Sudoku is a classic 9x9 Sudoku decorated with arrows. For every arrow, the digits along its path must add up to the digit in its circled cell. The standard row, column, and box rules still apply, so Arrow blends familiar Sudoku logic with light mental arithmetic. Unlike Killer Sudoku, digits may repeat along an arrow — only the sum matters — which gives the variant its own distinctive feel.
What is Arrow Sudoku?
Arrow Sudoku is played on the same 9x9 grid as standard Sudoku, with a handful of arrows overlaid on the cells. Each arrow has a circle at one end and a shaft that runs along a path of connected cells to an arrowhead. The digit inside the circle equals the sum of the digits along the path. Because the circle carries the total, it is always the largest value on its arrow. Each puzzle has a single unique solution reachable by pure logic.
Arrow Sudoku Rules
- Standard Sudoku rules: Each row, each column, and each 3x3 box must contain the digits 1 through 9 exactly once.
- Arrow sum rule: The digits along an arrow's path add up to the digit in its circled cell.
- The circle is the total: The circled cell holds the sum, so it is always the largest digit on its arrow.
- Repeats allowed: A digit may appear more than once on a path, provided the normal row, column, and box rules still hold. Only the sum has to be exact.
Minimum and Maximum Path Sums
The two facts that drive most Arrow deductions are how small and how large a path can total.
- Minimum: every path cell is at least 1, so a path of k cells sums to at least k. The circle can therefore never be smaller than the number of path cells.
- Maximum: the circle is a single digit, so it can be at most the grid size (9). That caps the whole path — a long path forces small digits because there simply isn't room in a single-digit total.
| Path length (9x9) | Smallest possible circle | Consequence |
|---|---|---|
| 2 cells | 3 | Circle is 3–9; circle never holds 1 or 2 |
| 3 cells | 4 | Path digits stay low; e.g. 1+2+3 = 6 |
| 4 cells | 6 | A circle of 9 forces a path like 1+2+2+4 or 1+1+3+4 |
Solving Strategies
1. Read the circle first
The circle is a real Sudoku digit and the sum of its path, so it is doubly constrained. A low circle with a long path is nearly forced — a circle of 6 over a three-cell path can only be 1+2+3 in some order. Start where the circle is small relative to its path length.
2. Bound the path from both sides
Combine the minimum (one per cell) and maximum (the circle) sums. If a four-cell path already has 1 and 3 placed and its circle is 8, the remaining two cells must sum to 4 — only 1+3, 2+2, or 3+1 fit, all subject to Sudoku. Bounding shrinks the options rapidly.
3. Exploit allowed repeats
Repeats are legal, so a path can reuse a digit as long as the cells sit in different rows, columns, and boxes. This is the opposite of Killer and often the key insight: a circle of 4 over a two-cell path could be 1+3, 3+1, or 2+2 — don't discard the double.
4. Combine with standard Sudoku logic
Arrow sums narrow candidates; classic techniques place them. Alternate arrow logic with naked singles, hidden singles, and pointing pairs from our solving techniques library. Each unlocks the other.
Mini Arrow (6x6)
Mini Arrow brings the same sum-to-the-circle rule to a compact 6x6 grid using the digits 1 through 6 with 2x3 boxes. With a maximum digit of 6, the arithmetic stays small: a three-cell path can total at most 6, so it must be a low combination such as 1+2+3. That makes the sum rule easy to see, so Mini Arrow is the perfect introduction — read the full Mini Arrow Sudoku guide or jump into the playable 6x6 board.
Tips for Beginners
- 1 and 2 are never circles. Any cell inside a circle can immediately drop 1 and 2.
- Long path, small digits. The circle caps the total at 9 (or 6 on a mini), so long paths are full of small numbers.
- Remember repeats are legal. Unlike Killer, a path can reuse a digit — keep 2+2, 3+3, and friends in your candidate list.
- Solve the circle and the path together. Each constrains the other, so update both whenever you place a digit.
- Start with Mini Arrow. Small sums on a 6x6 grid teach the same logic much faster.
- Never guess. Every Arrow puzzle has a unique logical solution. If you stall, re-bound a long path.
Arrow Sudoku rewards a light touch with sums and a good eye for which end — circle or path — is more constrained. Once you internalise the minimum and maximum path sums and remember that repeats are allowed, the arrows become a precise solving path. Start small with Mini Arrow, and the full 9x9 puzzles will soon feel approachable.