Arrow Sudoku

Arrow Sudoku decorates the grid with little arrows, each starting from a circle. The rule is a single, elegant equation: the digit in the circle equals the sum of the digits along the arrow's shaft. There are usually very few given numbers, so the arrows themselves — read as running totals — are what carry you through the solve.

The rule: the circle is the sum

Follow any arrow from its circle to its tip. Add up the digits sitting on the shaft, and that total must equal the digit in the circle. In the example below, the arrow passes over a 3 and a 5, so the circle must hold 8. Everything else is ordinary Sudoku: every row, column and box still needs 1–9 exactly once.

Reading an arrow: what its length tells you

Before you know a single digit on a shaft, its length already limits the circle. A two-cell arrow must sum to at least 1 + 2 = 3, so its circle is 3 or more. A three-cell arrow needs at least 1 + 2 + 3 = 6, and — because the largest three different digits are 7, 8 and 9 — at most 24, though the circle itself can only be 9, so the shaft can never exceed 9 in total. That upper limit is the real workhorse: a long arrow forces small digits onto its shaft.

Combine that with the no-repeat rule and arrows become very tight. If a three-cell arrow lies entirely inside one row, its three shaft digits must all differ, so the only sets that sum to 9 or less are combinations like {1, 2, 3} (sum 6), {1, 2, 4} (7), {1, 2, 5} or {1, 3, 4} (8) and {1, 2, 6}, {1, 3, 5} or {2, 3, 4} (9). The 1 is almost always on a long shaft, and a 9 almost never is.

Bigger circles: two-digit sums

Some Arrow puzzles draw the circle over two cells (a "pill"), letting the sum reach into double digits — a shaft summing to 17 would fill a pill reading "1" then "7". The logic is unchanged; you just read the circle as a two-digit number. On a standard single-cell circle, though, the sum can never exceed 9, which keeps the arithmetic gentle.

Solving strategy

• Start with the longest arrows. They cap the circle low and force small digits onto the shaft.
• Place the 1 first. Long shafts almost always need a 1; ruling out where the 1 can't go is a fast opener.
• Treat the circle as a cage sum. The same combination thinking as Killer combinations applies to the shaft digits.
• Feed the grid. Each digit an arrow forces behaves like a given for its row, column and box — chase the singles it creates.

Common mistakes

• Summing the circle in. The circle is not part of the sum — only the shaft cells add up to it.
• Allowing repeats on a same-line shaft. Shaft digits may repeat only if they lie in different rows, columns and boxes; on a straight shaft inside one unit they must all differ.
• Overshooting the circle. On a single-cell circle the shaft can total at most 9 — a common slip is to let it run higher.
• Forgetting ordinary Sudoku. The arrow rule is an extra constraint layered on top of the usual row, column and box rules.

Can I play it here?

Not yet — Arrow Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile:

• Try the closely related Killer, which you can play right now.
• Browse all the Sudoku variants we do offer.
• Or print free puzzles from the printable PDF page.