Arrow Sudoku keeps every Classic rule: each row, column and 3×3 box holds 1 to 9 once. On top of that, arrows run through the grid, each starting in a circle. The digit in the circle equals the sum of the digits on its arrow. Digits may repeat along an arrow when the cells are in different rows, columns and boxes. The sums give away a lot, which is why an Arrow puzzle can start with as few as 10 clues.
The rules
Fill the 9×9 grid so that every row, every column and every 3×3 box holds the digits 1 to 9 exactly once, as in Classic Sudoku.
Each arrow starts in a circle. Add up the digits in the cells along the arrow, from the circle to the arrowhead: the total is the digit in the circle.
A digit can appear twice on one arrow if those two cells do not share a row, column or box. Where they do, the usual Sudoku rule applies.
What the arrows change
A circle is at least the smallest its arrow can add up to. Every cell is at least 1, so a circle with a three-cell arrow is at least 3, and at least 4 when two of those cells share a row, column or box, because they cannot both be 1.
Each arrow cell is at most the circle minus the rest of the arrow. A circle of 4 with three cells on its arrow leaves each of them only 1 or 2.
On this site every puzzle has 6 to 10 arrows with 2 to 4 cells each, drawn for that puzzle alone. They turn freely: 40% of their steps go corner to corner, and more than half of the arrows cross into another box.
How to solve it
Start with the bounds. Each circle is at least what its arrow adds up to with the smallest digits and at most what it adds up to with the largest. The candidates the board shows already follow the digits placed on each arrow.
Then list the ways an arrow can add up. A circle of 6 over two cells that share a row can only be 1 + 5 or 2 + 4 and the other way round, so neither cell can be 3. Next Step calls this Arrow Combinations and lights the arrow it means.
Solve the rest as in Classic: singles, locked candidates, pairs. Every digit you place on an arrow narrows its circle and the other cells, so look at the arrow again each time.
Worked examples
Three positions from real puzzles on this site, walked through by the same Next Step teacher you get in a game. Step through each one.
The arrow sets its circle
The circle at R5C3 is the sum of the digits along its arrow: R5C4 and R4C3.
A circle caps its arrow
The circle at R1C5 holds 4, the sum of the digits along its arrow: R2C5, R3C4 and R4C3.
Only some sums fit
List every way the arrow from R6C8 can add up, using only the candidates in its cells. R5C9 and R4C8 share a row, column or box, so they cannot repeat a digit.
The four levels
Arrow levels use the same technique scale as Classic, with the arrow sum counted as an Easy technique and the combinations as a Medium one. Every puzzle is solvable by logic alone, which is why there is no Diabolical level.
Classic techniques, unchanged
The houses are the Classic rows, columns and boxes, so every Classic technique works as it is. These lessons teach them:
Frequently Asked Questions
Is Arrow Sudoku harder than Classic?
Not by its levels: they use the same technique scale as Classic. The arrows give extra information, so the puzzles start with fewer clues.
Can a digit repeat on an arrow?
Yes, when the two cells are in different rows, columns and boxes. About one arrow in six on this site has a digit twice on it.
Which end is the circle?
The circle is where the arrow starts. The digits you add up run from the circle to the arrowhead; the circle itself is not part of the sum.
Can an arrow turn or go diagonally?
Yes. Each cell touches the next one along a side or at a corner, and an arrow can turn as it goes. Two arrows never cross.
Can two arrows share a cell?
Not on this site. Each cell is on at most one arrow, as a circle or as part of a path.
Are the clues symmetric?
Yes. Turn the grid half a turn and the clues land on clues. The arrows are drawn freely for each puzzle.
Why is there no Diabolical level?
Every Arrow puzzle on this site can be solved by logic, up to Extreme techniques. Diabolical puzzles need trial and error, so they are left out.
Which tools can I use?
All of them: pencil marks in corner or centre notation, candidates, Auto Check, Check Cell and Check Puzzle, and Next Step, which lights the arrow whenever it is the reason for a move.
Try one now. Easy is a good place to start.