CageDokuArrow Sudoku Rules and Solving Tips
By Andrew Boyko, developer of CageDoku · Updated
Arrow Sudoku adds one rule to classic Sudoku: the digits along each arrow must add up to the digit in the circle at its start. If you enjoy Killer Sudoku’s arithmetic, you will enjoy arrows.
The rules
- Every row, column and 3×3 box contains 1 to 9 once.
- The digits along an arrow add up to the digit in its circle.
- Digits may repeat along an arrow unless a Sudoku rule (same row, column or box) forbids it.
Technique 1: the circle sets a ceiling
The circle holds one digit, at most 9. Each cell on the arrow holds at least 1, so a cell on an arrow of n cells can hold at most 9 − (n − 1). On a 4-cell arrow no cell can be higher than 6, and on a 5-cell arrow none can be higher than 5.
Technique 2: the arrow sets a floor for the circle
An arrow with n cells has a sum of at least n, so the circle is at least n. An arrow with two cells needs a circle of at least 2, and if the two cells share a row, column or box they must differ, so the minimum sum is 1 + 2 = 3.
Technique 3: small circles give small digits
A circle of 3 on a two-cell arrow forces the arrow to be 1 and 2 in some order. A circle of 4 on a three-cell arrow must be 1, 1 and 2 in some order, so two of the cells hold a 1 and therefore cannot share a row, column or box. Always check which cells see each other.
Practice
Hints in CageDoku highlight the arrow and the circle and explain the arithmetic step by step. Try an Arrow puzzle in your browser for free.
Frequently asked questions
Can an arrow have repeated digits?
Yes, unless two cells on it share a row, column or box.
Can the circle be any digit?
Yes, but it must equal the sum of the arrow and be at most 9.
Practice it in CageDoku
Free, ad-free Killer Sudoku and seven more variants. Hints name the technique and highlight the cells, so you learn why a digit goes where it goes.